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Physics Semester I Final Review

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If each component of a vector is doubled, what happens to the angle of that vector? 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half ConcepTest 3.2a Vector Components I

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If each component of a vector is doubled, what happens to the angle of that vector? 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan = 2y/2x, which is the same as tan = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change? ConcepTest 3.2a Vector Components I

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ConcepTest 3.4aFiring Balls I ConcepTest 3.4a Firing Balls I A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest

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ConcepTest 3.4aFiring Balls I ConcepTest 3.4a Firing Balls I A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? 1) it depends on how fast the cart is moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest when viewed from train when viewed from ground vertical same horizontal velocity In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart.

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Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4b Firing Balls II

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Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon. ConcepTest 3.4b Firing Balls II

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The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4c Firing Balls III

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The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart. ConcepTest 3.4c Firing Balls III

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ConcepTest 3.5 Dropping a Package You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: quickly lag behind the plane while falling 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all

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You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: quickly lag behind the plane while falling 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all same horizontal velocity maintain x-direction Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x-direction, so they stay aligned. Follow-up: What would happen if air resistance were present? ConcepTest 3.5 Dropping a Package

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ConcepTest 3.6aDropping the Ball I From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height

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From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? 1) the “dropped” ball 2) the “fired” ball 3) they both hit at the same time 4) it depends on how hard the ball was fired 5) it depends on the initial height They both fall from the same height.Therefore, they will hit the ground at the same time. Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant – remember that the x and y motions are completely independent !! Follow-up: Is that also true if there is air resistance? ConcepTest 3.6aDropping the Ball I

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ConcepTest 3.6bDropping the Ball II In the previous problem, which ball has the greater velocity at ground level? 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown

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In the previous problem, which ball has the greater velocity at ground level? 1) the “dropped” ball 2) the “fired” ball 3) neither – they both have the same velocity on impact 4) it depends on how hard the ball was thrown same vertical velocity “fired” ball has a larger net velocity Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? ConcepTest 3.6bDropping the Ball II

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ConcepTest 3.6c Dropping the Ball III A projectile is launched from the ground at an angle of 30 o. At what point in its trajectory does this projectile have the least speed? 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant

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A projectile is launched from the ground at an angle of 30 o. At what point in its trajectory does this projectile have the least speed? 1) just after it is launched 2) at the highest point in its flight 3) just before it hits the ground 4) halfway between the ground and the highest point 5) speed is always constant smallest highest point y- component of the velocity is zero The speed is smallest at the highest point of its flight path because the y- component of the velocity is zero. ConcepTest 3.6c Dropping the Ball III

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ConcepTest 4.1aNewton’s First Law I ConcepTest 4.1a Newton’s First Law I 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because:

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There are forces acting on the book leaving no net force There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force. ConcepTest 4.1aNewton’s First Law I ConcepTest 4.1a Newton’s First Law I 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because:

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ConcepTest 4.1bNewton’s First Law II ConcepTest 4.1b Newton’s First Law II 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero A hockey puck slides on ice at constant velocity. What is the net force acting on the puck?

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constant velocity not accelerating no net force The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck. ConcepTest 4.1bNewton’s First Law II ConcepTest 4.1b Newton’s First Law II 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? Follow-up: Are there any forces acting on the puck? What are they?

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ConcepTest 4.7aGravity and Weight I ConcepTest 4.7a Gravity and Weight I 1) F g is greater on the feather 2) F g is greater on the stone 3) F g is zero on both due to vacuum 4) F g is equal on both always 5) F g is zero on both always What can you say about the force of gravity F g acting on a stone and a feather?

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The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight. ConcepTest 4.7aGravity and Weight I ConcepTest 4.7a Gravity and Weight I 1) F g is greater on the feather 2) F g is greater on the stone 3) F g is zero on both due to vacuum 4) F g is equal on both always 5) F g is zero on both always What can you say about the force of gravity F g acting on a stone and a feather?

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1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always What can you say about the acceleration of gravity acting on the stone and the feather? ConcepTest 4.7bGravity and Weight II ConcepTest 4.7b Gravity and Weight II

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F/m mg g The acceleration is given by F/m so here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with acceleration g for both objects. 1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always What can you say about the acceleration of gravity acting on the stone and the feather? ConcepTest 4.7bGravity and Weight II ConcepTest 4.7b Gravity and Weight II Follow-up: Which one hits the bottom first?

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ConcepTest 4.9aGoing Up I ConcepTest 4.9a Going Up I A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg 2) N = mg 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator m v

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no net force NmgNmg The block is moving at constant speed, so it must have no net force on it. The forces on it are N (up) and mg (down), so N = mg, just like the block at rest on a table. ConcepTest 4.9aGoing Up I ConcepTest 4.9a Going Up I A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg 2) N = mg 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator m v

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A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg 2) N = mg 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator ConcepTest 4.9bGoing Up II ConcepTest 4.9b Going Up II m a

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net upward force Nmg Nmg net upward force The block is accelerating upward, so it must have a net upward force. The forces on it are N (up) and mg (down), so N must be greater than mg in order to give the net upward force! 1) N > mg 2) N = mg 3) N < mg (but not zero) 4) N = 0 5) depends on the size of the elevator F = N – mg = ma > 0 N > mg m a > 0 mg N A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? ConcepTest 4.9bGoing Up II ConcepTest 4.9b Going Up II Follow-up: What is the normal force if the elevator is in free fall downward?

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ConcepTest 4.10Normal Force ConcepTest 4.10 Normal Force Case 1 Case 2 Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle . In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface

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down in addition to mg larger up lessened In Case 1, the force F is pushing down (in addition to mg), so the normal force needs to be larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. ConcepTest 4.10Normal Force ConcepTest 4.10 Normal Force Case 1 Case 2 Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle . In which case is the normal force greater? 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface

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ConcepTest 4.11On an Incline ConcepTest 4.11 On an Incline 1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) Consider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater?

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1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) N W WyWy x y f ConcepTest 4.11On an Incline ConcepTest 4.11 On an Incline Consider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater? Case AN = W Case B N < W In Case A, we know that N = W. In Case B, due to the angle of the incline, N < W. In fact, we can see that N = W cos( ).

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ConcepTest 4.12Climbing the Rope ConcepTest 4.12 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down

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When you pull down on the rope, the rope pulls up on you!! reaction rope on youyou exerted on the rope When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the “reaction” force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton’s Third Law. ConcepTest 4.12Climbing the Rope ConcepTest 4.12 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your initial velocity, which is already upward 2) you don’t go up, you’re too heavy 3) you’re not really pulling down – it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down

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ConcepTest 4.14aCollision Course I ConcepTest 4.14a Collision Course I A small car collides with a large truck. Which experiences the greater impact force? 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each

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ConcepTest 4.14aCollision Course I ConcepTest 4.14a Collision Course I A small car collides with a large truck. Which experiences the greater impact force? 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each According to Newton’s Third Law, both vehicles experience the same magnitude of force.

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1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each In the collision between the car and the truck, which has the greater acceleration? ConcepTest 4.14bCollision Course II ConcepTest 4.14b Collision Course II

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1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each In the collision between the car and the truck, which has the greater acceleration? ConcepTest 4.14bCollision Course II ConcepTest 4.14b Collision Course II F/mcar larger acceleration smaller mass We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, since it has the smaller mass.

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ConcepTest 4.21Going Sledding ConcepTest 4.21 Going Sledding 1 2 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this?

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ConcepTest 4.21Going Sledding ConcepTest 4.21 Going Sledding 1 2 pushing down normal force is larger pulling up normal force is lessened In Case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the frictional force is proportional to the normal force. 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this?

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ConcepTest 4.22Will it Budge? ConcepTest 4.22 Will it Budge? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move A box of weight 100 N is at rest on a floor where s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? T m Static friction ( s = 0.4 )

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maximum s N = 40 N 30 N The static friction force has a maximum of s N = 40 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction. ConcepTest 4.22Will it Budge? ConcepTest 4.22 Will it Budge? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move A box of weight 100 N is at rest on a floor where s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? T m Static friction ( s = 0.4 ) Follow-up: What happens if the tension is 35 N? What about 45 N?

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1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? Net Force Normal Weight ConcepTest 4.23aSliding Down I ConcepTest 4.23a Sliding Down I

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1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? Net Force Normal Weight component of weight parallel to the plane increases component perpendicular to the plane decreases friction force gets smallerforce pulling the box down the plane gets bigger l As the angle increases, the component of weight parallel to the plane increases and the component perpendicular to the plane decreases (and so does the normal force). Since friction depends on normal force, we see that the friction force gets smaller and the force pulling the box down the plane gets bigger. ConcepTest 4.23aSliding Down I ConcepTest 4.23a Sliding Down I

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Is it possible to do work on an object that remains at rest? 1) yes 2) no ConcepTest 5.1 To Work or Not to Work

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Is it possible to do work on an object that remains at rest? 1) yes 2) no force acts over a distance no displacementno work done Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done. ConcepTest 5.1 To Work or Not to Work

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ConcepTest 5.2a Friction and Work I 1) friction does no work at all 2) friction does negative work 3) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

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f N mg displacement Pull opposite negative W = F d cos = 180 o W < 0 Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work (W = F d cos ), since = 180 o, then W < 0. ConcepTest 5.2a Friction and Work I 1) friction does no work at all 2) friction does negative work 3) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

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Can friction ever do positive work? 1) yes 2) no ConcepTest 5.2b Friction and Work II

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Can friction ever do positive work? 1) yes 2) no moves along with the truck force of friction that is making the box move Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move. ConcepTest 5.2b Friction and Work II

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In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work ConcepTest 5.2c Play Ball!

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In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work opposite in direction to the displacement of the ball, so the work is negative W = F d cos = 180 o W < 0 The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos ), since = 180 o, then W < 0. Note that because the work done on the ball is negative, its speed decreases. ConcepTest 5.2c Play Ball! Follow-up: What about the work done by the ball on the catcher?

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ConcepTest 5.2d Tension and Work 1) tension does no work at all 2) tension does negative work 3) tension does positive work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

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ConcepTest 5.2d Tension and Work 1) tension does no work at all 2) tension does negative work 3) tension does positive work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? v T perpendicular W = F d cos = 180 o W < 0 No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos ), since = 180 o, then W < 0. Follow-up: Is there a force in the direction of the velocity?

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ConcepTest 5.3 Force and Work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

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ConcepTest 5.3 Force and Work N f T mg displacement Any force not perpendicular to the motion will do work: no work N does no work positive T does positive work f does negative work mg does negative work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

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ConcepTest 5.8a Slowing Down 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases.

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F d = W net = KE = 0 – 1/2 mv 2 |F| d = 1/2 mv 2 thus: |F| d = 1/2 mv 2 doubles Therefore, if the speed doubles, four times larger the stopping distance gets four times larger. ConcepTest 5.8a Slowing Down 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases.

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ConcepTest 5.13 Up the Hill 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path?

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Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. ConcepTest 5.13 Up the Hill 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why?

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ConcepTest 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 1 4) same speed for all balls 2 3

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ConcepTest 5.16 Down the Hill same initial gravitational PE same height same final KEsame speed All of the balls have the same initial gravitational PE, since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv 2 ). Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 1 4) same speed for all balls 2 3 Follow-up: Which ball takes longer to get down the ramp?

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ConcepTest 5.18a Water Slide I 1) Paul 2) Kathleen 3) both the same Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose velocity is greater? Conservation of Energy: E i = mgH = E f = 1/2 mv 2 E i = mgH = E f = 1/2 mv 2 gH = 1/2 v 2 therefore: gH = 1/2 v 2 same height same velocity Since they both start from the same height, they have the same velocity at the bottom.

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ConcepTest 5.18b Water Slide II Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? 1) Paul 2) Kathleen 3) both the same

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ConcepTest 5.18b Water Slide II Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? Kathleen is at a lower height than Paul for most of her ride larger velocity Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus she always has a larger velocity during her ride and therefore arrives earlier! 1) Paul 2) Kathleen 3) both the same

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ConcepTest 5.21a Time for Work I 1) Mike 2) Joe 3) both did the same work Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

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same forcesame displacementsame amount of workTime does not matter for determining the work done Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done. ConcepTest 5.21a Time for Work I 1) Mike 2) Joe 3) both did the same work Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

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Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power ConcepTest 5.21b Time for Work II

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Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power Mike produced 0.5 W Joe produced 0.6 W Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower. ConcepTest 5.21b Time for Work II

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ConcepTest 5.22b Energy Consumption Which contributes more to the cost of your electric bill each month, a 1500-Watt hair dryer or a 600- Watt microwave oven? 1) hair dryer 2) microwave oven 3) both contribute equally 4) depends upon what you cook in the oven 5) depends upon how long each one is on 1500 W 600 W

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energy you have to know how long it was running We already saw that what you actually pay for is energy. To find the energy consumption of an appliance, you must know more than just the power rating—you have to know how long it was running. ConcepTest 5.22b Energy Consumption Which contributes more to the cost of your electric bill each month, a 1500-Watt hair dryer or a 600-Watt microwave oven? 1) hair dryer 2) microwave oven 3) both contribute equally 4) depends upon what you cook in the oven 5) depends upon how long each one is on 1500 W 600 W

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A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to ConcepTest 6.3a Momentum and Force

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A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to The rate of change of momentum is, in fact, the force. Remember that F = p/ t. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same. ConcepTest 6.3a Momentum and Force

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1) greater than 2) less than 3) equal to ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity?

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1) greater than 2) less than 3) equal to The rate of change of velocity is the acceleration. Remember that a = v/ t. The acceleration is related to the force by Newton’s 2 nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive. ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity?

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ConcepTest 6.4 Collision Course 1) the car 2) the truck 3) they both have the same momentum change 4) can’t tell without knowing the final velocities A small car and a large truck collide head-on and stick together. Which one has the larger momentum change?

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p = 0car and truck combined p ca equal and opposite– p truck Since the total momentum of the system is conserved, that means that p = 0 for the car and truck combined. Therefore, p car must be equal and opposite to that of the truck (– p truck ) in order for the total momentum change to be zero. Note that this conclusion also follows from Newton’s 3 rd Law. ConcepTest 6.4 Collision Course 1) the car 2) the truck 3) they both have the same momentum change 4) can’t tell without knowing the final velocities A small car and a large truck collide head-on and stick together. Which one has the larger momentum change? Follow-up: Which one feels the larger acceleration?

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ConcepTest 6.6 Watch Out! You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head- on). What should you do? 1) hit the other car 2) hit the wall 3) makes no difference 4) call your physics teacher! 5) get insurance!

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both time tforce exerted on YOU In both cases your momentum will decrease to zero in the collision. Given that the time t of the collision is the same, then the force exerted on YOU will be the same!! truckhitting the wallmosquito running him down If a truck is approaching at 30 mph, then you’d be better off hitting the wall in that case. On the other hand, if it’s only a mosquito, well, you’d be better off running him down... ConcepTest 6.6 Watch Out! You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do? 1) hit the other car 2) hit the wall 3) makes no difference 4) call your physics teacher! 5) get insurance!

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A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? 1) the beanbag 2) the rubber ball 3) both the same ConcepTest 6.7 Impulse

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A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? 1) the beanbag 2) the rubber ball 3) both the same change in momentum for the ball is greater, because of the rebound Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. The impulse delivered by the ball is twice that of the beanbag. For the beanbag: p = p f – p i = 0 – (–mv ) = mv For the rubber ball: p = p f – p i = mv – (–mv ) = 2mv ConcepTest 6.7 Impulse Follow-up: Which one imparts the larger force to the floor?

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ConcepTest 6.9a Going Bowling I p p 1) the bowling ball 2) same time for both 3) the ping-pong ball 4) impossible to say A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?

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ConcepTest 6.9a Going Bowling I We know: F psame Here, F and p are the same for both balls! same amount of time It will take the same amount of time to stop them. p p p = F av t so p = F av t 1) the bowling ball 2) same time for both 3) the ping-pong ball 4) impossible to say A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? av tt pp F

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ConcepTest 6.9b Going Bowling II p p stopping distance A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater? 1) the bowling ball 2) same distance for both 3) the ping-pong ball 4) impossible to say

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ConcepTest 6.9b Going Bowling II p p W = KE less massgreater speed(why?)greater KE(why again?) W = Fd same less massive ballbigger Use the work-energy theorem: W = KE. The ball with less mass has the greater speed (why?), and thus the greater KE (why again?). In order to remove that KE, work must be done, where W = Fd. Since the force is the same in both cases, the distance needed to stop the less massive ball must be bigger. stopping distance A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater? 1) the bowling ball 2) same distance for both 3) the ping-pong ball 4) impossible to say

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ConcepTest 6.10a Elastic Collisions I v 2 v 1 at rest 1) situation 1 2) situation 2 3) both the same Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?

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Remember that the magnitude of the relative velocity has to be equal before and after the collision! ConcepTest 6.10a Elastic Collisions I v 1 1 golf ball bounce back with speed close to v In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v. v 2 2v2v 2 golf ball rebound with speed close to 2v In case 2 the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v. 1) situation 1 2) situation 2 3) both the same Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?

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ConcepTest 6.10b Elastic Collisions II Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball? 1) zero 2) v 3) 2v 4)3v 5) 4v

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relative velocity v v –2v +2vRemember that relative velocity has to be equal before and after collision! Before the collision, the basketball bounces up with v and the rubber ball is coming down with v, so their relative velocity is –2v. After the collision, it therefore has to be +2v!! ConcepTest 6.10b Elastic Collisions IIv v v v vv v 3v v (a)(b)(c) m M Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball? 1) zero 2) v 3) 2v 4)3v 5) 4v Follow-up: With initial drop height h, how high does the small rubber ball bounce up?

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ConcepTest 6.14b Recoil Speed II 1) 0 m/s 2) 0.5 m/s to the right 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

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ConcepTest 6.14b Recoil Speed II Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. p cannonball = (10 kg)(50 m/s) = 500 kg-m/s (0.5 m/s) p flatcar = 500 kg-m/s = (1000 kg)(0.5 m/s) 1) 0 m/s 2) 0.5 m/s to the right 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

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When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired) 1) it is much sharper than the gun 2) it is smaller and can penetrate your body 3) it has more kinetic energy than the gun 4) it goes a longer distance and gains speed 5) it has more momentum than the gun ConcepTest 6.15 Gun Control

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When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired) 1) it is much sharper than the gun 2) it is smaller and can penetrate your body 3) it has more kinetic energy than the gun 4) it goes a longer distance and gains speed 5) it has more momentum than the gun While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v 2, the bullet has considerably more KE and therefore can do more damage on impact. ConcepTest 6.15 Gun Control

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ConcepTest 6.16a Crash Cars I 1) I 2) II 3) I and II 4) II and III 5) all three If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt?

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ConcepTest 6.16a Crash Cars I In case I, the solid wall clearly stops the car. since p tot = 0 before the collision p tot must also be zero after the collision In cases II and III, since p tot = 0 before the collision, then p tot must also be zero after the collision, which means that the car comes to a halt in all three cases. 1) I 2) II 3) I and II 4) II and III 5) all three If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt?

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ConcepTest 6.16b Crash Cars II If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)? 1) I 2) II 3) III 4) II and III 5) all three

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ConcepTest 6.16b Crash Cars II case III KE = 1/2 m v 2 case III largest velocity The car on the left loses the same KE in all 3 cases, but in case III, the car on the right loses the most KE because KE = 1/2 m v 2 and the car in case III has the largest velocity. If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)? 1) I 2) II 3) III 4) II and III 5) all three

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ConcepTest 6.17 Shut the Door! 1) the superball 2) the blob of clay 3) it doesn’t matter -- they will be equally effective 4) you are just too lazy to throw anything You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?

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ConcepTest 6.17 Shut the Door! soits p (and that of the door) is 2mv The superball bounces off the door with almost no loss of speed, so its p (and that of the door) is 2mv. soits p is less than that of the superball The clay sticks to the door and continues to move along with it, so its p is less than that of the superball, and therefore it imparts less p to the door. 1) the superball 2) the blob of clay 3) it doesn’t matter -- they will be equally effective 4) you are just too lazy to throw anything You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it?

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