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10/28/2013 And so it comes to this, the mind blowing Sir Isaac Newton and his laws of motion And so it comes to this, the mind blowing Sir Isaac Newton and his laws of motion Bullseye Lab

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An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

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Center of gravity (mass)

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10/29/2013 Homework ?’s That’s some good inertia What is this Force? (not that force) Newton’s 1 st and 2 nd Law Demos Bullseye Lab

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What is a Force?

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First Law - Inertia Law of Inertia – every object continues in a state of rest, or of motion in a straight line at a constant speed, unless it is compelled to change that state by forces exerted upon it.

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Inertia Concepts Mass – the more mass an object has, the greater its inertia and the more force it takes to change its state of motion. Mass is the measure of the inertia of an object.

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The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

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F = ma Mass = kg Acceleration = m/s 2 Force = kg ·m/s 2 Newton (N) = kg ·m/s 2

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10/30/2013 Bullseye Lab Shooting the Moon Newton’s Third Law

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Second Law of Motion Newton was the first to realize that the acceleration produced when we move something depends not only on how hard we push or pull, but also on the object’s mass. The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force and is inversely proportional to the mass of the object.

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Problem #8 on page 124

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p. 125 #21

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11/1/13 – Finish Bull’s Eye Lab – Shooting the Moon – Normal Force Tug of war physics, oh…okay Vectors in multiple directions!

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How much force is needed to keep a 20-N stone from falling? F = 20 N

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3. What applied force accelerates a 20-kg stone straight up at 10 m/s 2 ? 9.8 m/s 2 F net = F up + F down F up = F net - F down F up F down F up = ma net - ma down F up = m(a net - a down ) F net

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F up = 20kg[10m/s 2 -(-9.8m/s 2 )] F up = 20kg[19.8 m/s 2 ] F up = 396 N 9.8 m/s 2

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4 m/s 2 W = 9800 N 4. A rocket weighs 9800 N a) What is its mass? W = mg m = 9800n/9.8m/s 2 m = 1000 kg m= W/g

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4 m/s 2 W = 9800 N 4. A rocket weighs 9800 N b) What force gives it a vertical acceleration of 4 m/s 2 ? F net = F up + F down F up = F net - F down F up = ma net - F down

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4 m/s 2 F up = (1000 kg·4 m/s 2 ) - (-9800 N) F up = 4000 N + 9800 N F up = 13800 N

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Whenever a first body exerts a force F on a second body, the second body exerts a force - F on the first body. F and –F are equal in magnitude but opposite in direction. The law of action reaction

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Interaction Pairs Two forces that are in opposite directions have equal magnitude. You push your friend, this does not cause your friend to exert a force on you. The forces exist together or not at all.

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Free Body Diagrams

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11/5/13 – Third Law Thought Experiment – Shooting the Moon – Normal Force Tug of war physics, oh…okay Vectors in multiple directions!

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Magnetic cart moves its self Or Blow your own sail Thought Experiment

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Plane Free Body Diagram

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Normal Force The perpendicular contact force exerted by a surface on another object.

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11/6/13 – Thought Experiment – Drag Force – Tension on strings Tug of war physics, oh…okay Vectors in multiple directions!

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According to legend, a horse learned newton's laws. When the horse was told to pull a cart, it refused, saying that if it pulled the cart forward, according to Newton's third law, there would be an equal force backwards: thus there would be balanced forces, and the cart would not accelerate. How would you reason with this horse?

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Goals for Chapter 5 To study conditions that establish equilibrium. To study applications of Newton’s Laws as they apply when the net force is not zero. To consider contact forces and the effects of friction. To study elastic forces (such as spring force). To consider forces as they subdivide in nature (strong, electromagnetic, weak, and gravitational).

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Dog Fight Susan is holding her dog, its’ mass is 8.0 kg, when Allen decides that he wants it and tries to pull it away from Susan. If Allen pulls horizontally on the dog with a force of 10 N and Susan pulls with a horizontal force of 11 N in the opposite direction, what is the horizontal acceleration of the dog?? Why doesn’t the dog bite one of them?

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Tension: – A specific name for the force exerted by a string or rope. Forces on Ropes and Strings

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Tension: – A specific name for the force exerted by a string or rope. Forces on Ropes and Strings

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Superhero Tension Situations

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11/6/13 – Thought Experiment – Drag Force – Tension on strings Tug of war physics, oh…okay Vectors in multiple directions!

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Problem 4 on page 152

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Two dimensional equilibrium – Example 5.2 Both x and y forces must be considered separately. Follow worked example 5.2 on page 130.

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Two dimensional equilibrium – Example 5.2

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p.153 # 14a

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# 13 on 153

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11/12/13 Newton’s Laws in the real world – Drag Force – Inclined Planes Friction Tug of war EQUALIBRIUM Vectors in multiple directions!

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Drag Force Is it true that particles in the air around an object exert forces on it? Yes, a huge force, but they all balance, and there is no net effect. What if the object is moving through the air? – It experiences a drag force Drag Force: the force exerted by a fluid on an object moving through a fluid. There is a direct relationship between the magnitude of the drag force and the surface area of a moving object.

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Terminal Velocity The constant velocity that is reached when the drag force equals the force of gravity.

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Inclined Plane Force Components

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11/13/2013 Newton’s Laws in static and dynamic situations Sample problems Contact Forces Friction Circular motion lab

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Problem in the back of the room

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What is Friction? Friction is the force resisting the relative lateral (side to side) motion of solid surfaces, fluid layers, or material elements in contact. So far we have neglected friction, but since it is all around us, it is worth treating.

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Two Main Types of Friction Push a book across a desk, it experiences a type of friction that acts on all moving bodies. KINETIC FRICTION (F k ) a force that is exerted by one surface against another when the two surfaces rub against each other because one or both of the surfaces are moving.

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Two Main Types of Friction Now try pushing a heavy couch across the floor, give it a push, and it stays where it is. Why? STATIC FRICTION (F s ) the force exerted on one surface by another when there is no motion between the two surfaces.

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Pull a block of known mass along a table at a constant velocity, stack more blocks on top to increase the normal force and note the effect. If you do all this, collect your data and then try it with different surfaces coming into contact with the table, you can make a graph like this one. Normal Force Kinetic frictional force Highly Polished Table Rough Table Sandpaper Kinetic Frictional Force vs. Normal Force The slope of each line is related to the magnitude of the resulting frictional force. The steeper the slope, the greater the force needed to pull the object across the surface.

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11/14/2013 Contact Forces Friction Sample problems Circular motion lab

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The conditions for a particle to be in equilibrium Necessary conditions for an object to settle into equilibrium (all things in balance, no change in motion): F = 0 Components must be balanced as well: F x = 0 and F y = 0

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What does the slope represent? In this case the slope represents the coefficient of kinetic friction. We use it to find Kinetic Friction Force (F k ), as follows: Highly Polished Table Rough Table Sandpaper Kinetic Frictional Force vs. Normal Force

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Maximum Static Friction Force is related to the normal force in a similar way. Static Friction Force (F s )is the force that responds to a force trying to cause a stationary object to move. If no force is acting on an object, F s is zero. If a force begins to act on an object, then F s will increase to a maximum value before it is overcome and the object will begin moving. We calculate F s using the coefficient of static friction as follows:

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Get in the chair so we can do some Physics!

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Superman Problem A train is approaching a washed out railroad bridge and it is accelerating uncontrollably at 2 m/s 2. Superman arrives just in time and begins pushing on the front of the train when there is only 500 m of track left. a.Assuming Superman causes the 750,000 kg train to uniformly decelerate from 30 m/s to 0 m/s just in time to keep from going off the end of the track, what total force did Superman have to apply to the train in order to stop it? b.If the coefficient of friction between the boots and the track is 0.99, what force must superman be applying to the ground?

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11/15/2013 Contact Forces Friction Sample problems Circular motion lab

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#36 on p.155

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Grasshopper Newton’s Third Law and the Grasshopper

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11/18/2013 Chapter 3 and 4 review Circular motion lab

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11/20/2013 Chapter 3 and 4 test make-up HW Question Friction Forces on inclines Circular motion lab

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11/21/2013 Chapter 3 and 4 test make-up today Circular motion lab due HW Questions? Friction Forces on inclines Extra Credit?

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A girl exerts a 36 N horizontal force as she pulls a 52 N sled across a cement sidewalk. What is the coefficient of kinetic friction between the sidewalk and the metal sled runners? Ignore air resistance.

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Lets look at problem #46

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An example involving two systems – Example 5.4 See the worked example on page 132 and 133. This example brings nearly every topic we have covered so far in the course.

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Logan on the icy hill Logan is at the top of an ice covered hill and he is wearing a slippery snow suit (very little friction between the two). Assuming he weights 15 kg and the hill is at a 20 degree angle to the horizontal, what is his acceleration down the hill?

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Now add friction A 62 kg person on skis is going down a hill sloped at 37. The coefficient of kinetic friction between the skis and the snow is 0.15. How fast is the skier going 5 s after starting?

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Problem 6 plus a little more

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A force of 60.0 N accelerates a 10 kg block at 3 m/s 2 along a horizontal surface. 1.How large is the friction force? 2.What is the coefficient of friction?

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11/22/2013 Elastic Forces TED thoughts Extra Credit?

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11/25/2013 Elastic Forces Wait you’re giving us HW? Extra Credit?

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The true Joy of Toys is the PHYSICS

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Hooke's law is the relationship between the force exerted on the mass attached to a spring and its position x. Consider a object with mass m, that is on a frictionless surface and is attached to a spring with spring constant k. The force the spring exerts on the mass depends on how much the spring is stretched or compressed, and so this force is a function of the mass's position. F s = kx

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k = F/ x F s = kx

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Problem 57 on page 156

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Problem # 59 on p. 156

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Problem 77 on page 158

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TED Albert Einstein (a nerd worth remembering) said, "the unleashed atom has changed everything except our way of thinking".

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W s = ½ F s x A = ½bh

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Problem # 38 on page 155 Tires on a road, rolling friction:

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11/20/2012 Homework ?’s Homework ?’s Practice with Friction Practice with Friction Apophis Apophis Friction Lab Friction Lab

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Elevator Problem Your mass is 75kg, and you are standing on a bathroom scale in an elevator. Starting from rest, the elevator accelerates upward at 2 m/s 2 for 2 seconds and then continues at a constant speed. Is the scale reading during the acceleration greater than, equal to, or less than the scale reading when the elevator is at rest?

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Shooting the Moon Mad Hatter Harry is sick of being watched by the man in the moon every night. So he sets out on a mission to rid him self of the moon once and for all. He is trying to build a cannon that can shoot the peeping tom in the sky. If the combustion process of the cannon’s “fuel” takes 0.2 seconds, the cannon ball is 20 kg, and escape velocity is 11,201 m/s. What magnitude of force must he impart on the cannon shell?

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11/2/12 – Bullseye reward – Horse and Buggy Problem – Elevator Problem Tug of war physics, oh…okay New Lab: Circular motion

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11/5/12 – Bullseye reward? – Old Homework Tug of war physics, oh…okay Chapter 5 application of Newton’s Three Laws New Lab: Circular motion

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11/6/2012 Old Homework Applying Newton’s Three Laws Circular motion lab

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11/7/2012 Watch Inclined Plane Force Components on YouTube from KhanAcademy.org Practice Problem in back Forces not in equilibrium

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11/9/2012 Projectile motion problem solving. Newton’s Laws in dynamic situations Sample problems Circular motion lab

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Air cannon problem How fast is the air cannon shooting? – Find horizontal and vertical components, then velocity. What kind of information can we get from experimentation?

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Problem 19 on 153

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Problem 22 conceptually in back.

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11/13/2012 Test on Chap 3 and 4 Circular motion lab

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Nate is driving along a cliff side road when a wayward moose crosses his path. Nate slams on the brakes and swerves into the guard rail. He gets out to inspect the damage and sees the front right side of his car is completely wrecked. In frustration he throws his keys horizontally at 8 m/s off a 64 meter high cliff. How far from the base of the cliff should Nate look for his keys?

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An outfielder is throwing a baseball to the third baseman. The ball is released from shoulder height with an initial velocity of 29.4 m/s at an initial angle of 30° with respect to the ground. If the ball flies through the air for 3 seconds before being caught by the third baseman at an equal shoulder height, what was the maximum height of the ball above the outfielders shoulder height as it flew through the air?

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The mass of the space shuttle is approximately 2.0 x 106 kg. During lift-off, the net force on the shuttle is 1.0 x 107 N directed upward. What is the velocity of the shuttle 10 s after lift-off?

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A 50-kg woman wearing a seat belt is traveling in a car that is moving with a velocity of 10 m/s. In an emergency, the car is brought to a stop in 0.5 s. What force does the seat belt exert on the woman so that she remains in her seat?

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What is the mass of an object weighing 196 N?

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A 15-kg mass weighs 60.0 N on Planet X. The mass is allowed to fall freely from rest near the surface of the planet. What will be the velocity of the mass after falling for 6.0 seconds?

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11/15/2012 Test Lab due Monday Homework Problem Friction and motion Two main types of friction Friction Lab

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Number 12 on page 153. In a rescue, the 73 kg police officer is suspended by two cables as shown below. a)Sketch a free body diagram of the officer. b)Find the tension in each cable.

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11/16/2012 Test Grades Lab due Monday Friction Problems Friction Lab

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11/26/12 New Homework Test Make-up Question and review session (Tues. and Wed. after school) Elastic Forces (Phet Demo) Friction Lab

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11/27/12 New Homework Test Make-up Question and review session (Tues. and Wed. after school) Friction Lab

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p. 166 Rounding the curve

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p. 167 Rounding a banked curve

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Forces in Dynamics An object is no longer in equilibrium due to forces acting on it. Same as the things we have discussed before, now we just apply Newton’s Laws. Can you think of any examples of an object experiencing unbalanced forces?

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TUG OF WAR Ok, look at the team on the left (team A), they are exerting a force of 500 N. If the rope does not move then the team on the right (team B) must also be exerting a force of 500 N. What is the tension on the rope? 1000N?

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Think of the ropes cut in two halves. The left hand is not moving, so the net force is 0. Thus, F A on rope = F right on left = 500 N. Similarly, F B on rope = F left on right = 500 N. But the two tensions F right on left and F left on right are an interaction pair, so they are equal and opposite. So the tension on the rope equals the force each team pulls with, 500 N.

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Goals for Chapter 6 To understand the dynamics of circular motion. To study the unique application of circular motion as it applies to Newton’s Law of Gravitation. To examine the idea of weight and relate it to mass and Newton’s Law of Gravitation. To study the motion of objects in orbit as a special application of Newton’s Law of Gravitation.

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A review of the relationship between v and a c. The velocity changes direction, not magnitude.

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a c = v 2 /r

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The force needed to keep an object moving in a circular path is called the centripetal force. It is the force that produces the acceleration and is always directed toward the center. F c = mv 2 /r

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In terms of the force of gravity and centripetal force what is happening in the cup?

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What centripetal force is needed to keep a 4-kg mass moving at a constant speed of 3 m/s in a circle having a radius of 8 m? F c = mv 2 /r F c = (4 kg)(3 m/s) 2 /8 m F c = 4.5 kg-m/s 2 F c = 4.5 N Practice

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Notice how v becomes linear when F c vanishes.

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11/29/12 Homework Questions? Circular Motion Cavendish Measures Gravity Force of gravity between two objects Objects in orbit What about the guy that said there is no gravity?

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A frictionless rollercoaster does a vertical loop with a radius of 6.0m. What is the minimum speed that the roller coaster must have at the top of the loop so that it stays in touch with the rail? mv 2 /r = mg F c = 0 + F g g = v 2 /r v = 7.7 m/s F net = F N + F g v 2 = gr v 2 = 9.8 m/s 2 x 6 m Practice

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A B C Draw free-body diagrams at each location on the roller coaster.

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What is the net force on the rider at point A? What is F net at point A also called? What is F N at point A acting on the rider(apparent weight)? What velocity is needed at point A to produce an F N on the rider of 0? F net = -F g + (F N ) F net = F centripetal F N = F g - F c 0 = F g - F c F g = F c mg = mv 2 /r v = (gr) ½ A

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What is the net force on the rider at point B? What is F net at point B also called? What is F N at point B acting on the rider(apparent weight)? What is the “g-force” at point B? F net = F N + (-F g ) F net = F centripetal F N = F c + F g G-force = F N / F g B

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What is the net force on the rider at point C? What is F net at point C also called? What is F N at point C acting on the rider? What does a negative F N mean? F net = F N + F g F net = F centripetal F N = F c - F g - F N = “I’m falling” C

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Newton and Gravity

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11/30/12 New Homework Force of gravity between two objects Objects in orbit Does Gravity exist? Gravitation Lab

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M1M1 M2M2 R F g = GM 1 M 2 R2R2 F g =mg

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m1m1 m2m2 R F g = F g = m 2 g R2R2 Gm 1 m 2 m 2 g = Gm 1 m 2 R2R2 g = Gm 1 R2R2

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MeMe m2m2 R g = G M e R2R2

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MeMe m2m2 R g =g = 6.7 x 10- 11 Nm 2 /kg 2 (6.0 x 10 24 kg) ( 6.4 x 10 6 m) 2

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MeMe m2m2 R g =g =9.8 m/s 2

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50 kg6 kg 2.0 m F g = GM 1 M 2 R2R2

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50 kg6 kg 2.0 m Fg =Fg = 6.7 x 10- 11 Nm 2 /kg 2 (50 kg)(6 kg) (2 m) 2

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50 kg6 kg 2.0 m Fg =Fg = 5.0 x 10- 8 N

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It looks like a shooting star The International space station is orbiting above the Earth at approximately 350 km. If it has a mass of 450000 kg, what is the force of gravity between it and the Earth? SEE IT?SEE IT?

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It looks like a shooting star Given your answer to the following question, how fast must the ISS be moving to stay in orbit?

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m1m1 m2m2 R F g = F g = m 2 g R2R2 Gm 1 m 2 m 2 g = Gm 1 m 2 R2R2 g = Gm 1 R2R2

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M1M1 M2M2 R F g = GM 1 M 2 R2R2 100 kg 50 kg 1.0 m

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M1M1 M2M2 R 100 kg 50 kg 1.0 m Fg =Fg = 6.7 x 10 -11 Nm 2 /kg 2 (50 kg)(100 kg) (1.0 m) 2 Fg =Fg = 3.35 x 10 -7 N

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M1M1 M2M2 R 100 kg 50 kg 1.0 m Fg =Fg = 3.35 x 10 -7 N = 50 kg x g g = 6.7 x 10 -9 m/s 2

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M1M1 M2M2 R 100 kg 50 kg 1.0 m Fg =Fg = 3.35 x 10 -7 N = 100 kg x g g = 3.35 x 10 -9 m/s 2

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A radioactive cesium nucleus emits a beta particle of mass 9.1 x 10 -31 kg and transmutes (changes) into a barium nucleus that has a mass of 2.2 x 10 -25 kg. What is the gravitational force of attraction between the barium nucleus and the beta particle when they are 2.0 x 10 -8 m apart? Based on your answer, is the force of gravity important in holding subatomic particles together? Explain. Concept Problem #5

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3.3 x 10 -50 N

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12/15/11 Lunar Mystery question Homework Pass back Old Homework Universal Gravitation practice What about the guy that said there is no gravity?

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Jupiter and Earth Jupiter is 5.2 times farther from the Sun than Earth. Find Jupiter’s orbital period in Earth yrs.

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g =g = GM R2R2

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Orbiting the Earth To maintain a constant distance around the Earth, a satellite must maintain a certain speed. If it did not it would fall into the atmosphere. We can determine the speed with which something orbits the Earth by the radius of its orbit.

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Orbiting the Earth We can also use the radius of a satellites orbit to determine the period of its orbit.

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A satellite is in orbit around a small planet. The orbital radius is 6.7 X 10 4 km and its speed is 2.0 X 10 5 m/s. What is the mass around which the satellite orbits?

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Gravity is all around A moon in orbit around a planet, like ours, experiences a gravitational force not only from the planet, but also from the Sun. The illustration below shows a moon during a solar eclipse, when the planet, the moon and the Sun are aligned. The moon has a mass of 3.9x10 21 kg, the planet is 2.4x10 26 kg and the Sun is 2.0x10 30 kg. The distance from the moon to the center of the planet is 6.0x10 8 m. The moon to the Sun is 1.5x10 11 m. What is the ratio of the gravitational force on the moon due to the planet compared to the gravitational force on the moon due to the Sun?

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12/16/11 Lunar Mystery question Universal Gravitation practice Newton/Einstein Gravity What about the guy that said there is no gravity?

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R (x = distance stretched = d) W s = F s x d F s = kx W s = ½ F s x W s = PE s = ½ kx 2

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What does Frictional Force depend on? Plays a role Does not Play a role

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What does Frictional Force depend on? Plays a role Does not Play a role

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11/16/11 Homework due tomorrow Friction sample problems Equilibrium and the Equilibrant Friction on an inclined plane Friction Lab

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Find the equilibrant

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More Feng shui Problem You need to move a 105 kg sofa to a different location in the room. It takes 102 N to start it moving. What is the coefficient of static friction between the sofa and the carpet?

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Simple Push Problem You push a box across a wooden floor at a constant speed of 1 m/s. The coefficient of kinetic friction between the box and floor is 0.2. How much force do you exert on the box?

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Simple Push Problem continued If you double the force you exerted on the box in the previous problem, what is the resulting acceleration of the box?

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When on a ramp, gravity must be broken into the effect it has on the angle of the ramp. Gravity is diluted by the angle of the ramp.

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11/17/11 Homework Nanotechnology Applications, things to ask about tomorrow. Friction on an inclined plane Friction Lab

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Apply motion to an inclined plane A crate that weighs 562 N is resting on a plane that is inclined 30 above the horizontal. Find the components of weight force that are parallel and perpendicular to the plane.

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Logan on a slide Logan, who has a mass of 15 kg, starts down a slide that is inclined at 45⁰ with the horizontal. If the coefficient of kinetic friction between the slide and Logan is 0.25, what is his acceleration?

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11/22/11 http://www.lifesaverusaonline.com/ Friction on an inclined plane Work: – Friction Lab – Homework – Case Study related assignment

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Pulling up a slope A 100N block is pulled up a ramp that is at a 45⁰ angle. The coefficient of friction is 0.3. What force is needed to move it up the ramp at a constant speed?

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10/23/11 Robots: just sayin’ Work: – Friction Lab – Homework – Case Study related assignment

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Accelerating Block The coefficient of kinetic friction between the block and the ramp is (0.20). The pulley is frictionless. What is the acceleration of the system?

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11/1/10 Hand in Homework Test on vectors and friction Go over Homework Pushing up a slope against friction and gravity Practice Problems Friction worksheet Projectile Motion

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When on a ramp, gravity must be broken into the effect it has on the angle of the ramp. Gravity is diluted by the angle of the ramp.

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Vertical Displacement (m) Horizontal Displacement (m) A stone is thrown at a speed of 10 m/s from the top of a 100 meter high cliff. a)How long does it take the stone to reach the bottom of the cliff? b)How far from the base of the cliff does the stone hit the ground? c)What are horizontal and vertical components of the stones velocity just before it hits the ground?

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