2 Topics to be covered Momentum & Impulse Linear momentum Conservation of MomentumMomentum is conservedElastic and Inelastic CollisionsCollisionsElastic Collisions
3 Overview What happens during a car crash? How do rockets work? my rocketCan physics improve our golf game?To answer these questions we introduce momentumEQ: Ultimately why is it hard to stop something that has a lot of momentum?
4 MomentumThe concept of force and Newton’s laws can be used to calculate how the motion of an object changes when the object is struck.We will examine how the force and the duration of the collision between two objects affect the motion of an object.
5 MomentumA brontosaurus has a lot of momentum, but so does a piece of hot lead shot from a rifle.We should expect than that momentum has something to do with an objects mass and velocity.P = momentum, it is a vector quantity.px = mvx & py = mvyRelated to kinetic energyDerive this equation
7 Pause for a Cause P = mv => 2250 kg * 25m/s = A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck?Given:m =2250 kgv = 25 m/s to the eastP = mv => 2250 kg * 25m/s =Practice A5.6 x 104 kg*m/s
8 Pause for a CauseCompare the momentum of a 6160 kg truck moving at 3.00 m/s to the momentum of a 1540 kg car moving at m/s.
9 Pause for a CauseA rubber ball with a mass of 0.30 kg is dropped onto a steel plate. The ball’s speed just before impact is 4.5 m/s and just after impact is 4.2 m/s. What is the change in the ball’s momentum?
10 Change in Momentum & Impulse A change is momentum take a forceIn fact Newton first expressed his second law not as…F = ma, butSolve for momentumThis state a force over time changes an objects momentum
11 Impulse = Momentum Momentum is defined as “Inertia in Motion” Ns Consider Newton’s 2nd Law and the definition of acceleration Units of Impulse: Units of Momentum:NsKg x m/sMomentum is defined as “Inertia in Motion”
12 Pause for a CauseA 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision.7.0 X 104 N to the eastPractice B
13 Pause for a CauseA player at first base catches a throw traveling 22 m/s. The baseball, which has a mass of kg, comes to a complete stop in the glove after s. Assuming the force of the glove was uniform, what force did the glove exert on the ball?
14 Pause for a CauseA 65 kg trapeze artist falls straight down onto a safety net. The trapeze artist’s initial speed as she hits the net is 9.9 m/s, and the net stretches 1.5 m vertically as she comes to a stop. What average net force does the trapeze artist experience while the net breaks her fall? How many “g’s” of acceleration does she experience on average? (1 g = 9.81 m/s )
15 Pause for a CauseA 100 g ball is dropped from a height of h = 2.00 m above the floor. It rebounds vertically to a height of h'= 1.50 m after colliding with the floor. (a) Find the momentum of the ball immediately before it collides with the floor and immediately after it rebounds, (b) Determine the average force exerted by the floor on the ball. Assume that the time interval of the collision is 0.01 seconds.
16 Stopping DistanceHighway safety engineers use the impulse-momentum theorem to determine stopping distances.ExampleTwo identical trucks both traveling at the same speedTruck 1 is carrying a load of bricks doubling the mass of the truck.Therefore the mathematical expression for this would beTruck 1 = 2(Truck 2)Or double the momentumTruck 1: stopping distance is double Truck 2Truck 1: stopping time is double Truck 2
17 Pause for a CauseA 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is N to the east? How far does the car travel during the deceleration?Unknown: Δt = ? Δx = ?m = 2240 kgvi = 20.0 m/s to the west,vi = −20.0 m/svf = 5.00 m/s to the west,vf = −5.00 m/sF = 8410 N to the east,F = N= 4.00s= 4.00s
18 Pause for a Cause = -50.0 m = or 50.0 m to the west A 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is N to the east? How far does the car travel during the deceleration?Unknown: Δt = ? Δx = ?m = 2240 kgvi = 20.0 m/s to the west,vi = −20.0 m/svf = 5.00 m/s to the west,vf = −5.00 m/sF = 8410 N to the east,F = NPractice C= m= or 50.0 m to the west
19 Impulse is the AreaIn real life the force on an object is rarely constant. Since I=Ft, Impulse is the AREA of a Force vs. Time graph.
20 Topics to be covered Momentum & Impulse Linear momentum Conservation of MomentumMomentum is conservedElastic and Inelastic CollisionsCollisionsElastic Collisions
21 Momentum is Conserved Ball A has velocity, ball B is sitting still After the collision ball A has transferred 97% of it’s momentum to ball b.
22 Conservation of Momentum For an isolated system, the law of conservation of momentum can be stated as follows:The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.
23 Pause for a Cause = -4.2 to the right A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?Given:m1 = 76 kgm2 = 45 kgv1,i = 0 v2,i = 0v1,f = 2.5 m/s to the rightUnknown: v2,f = ?Practice D= -4.2 to the right
24 Pause for a CauseAn astronaut with a mass of 85 kg is outside a space capsule when the tether line breaks. To return to the capsule, the astronaut throws a 2.0 kg wrench away from the capsule at a speed of 14 m/s. At what speed does the astronaut move toward the capsule?Practice D= 0.33 m/s
25 Pause for a Cause = 7.4x10-2 m/s A 65.0 kg ice-skater standing on frictionless ice throws a 0.15 kg snowball horizontally at a speed of 32.0 m/s. At what speed does the skater move backward?Practice D= 7.4x10-2 m/s
26 Topics to be covered Momentum & Impulse Linear momentum Conservation of MomentumMomentum is conservedElastic and Inelastic CollisionsCollisionsElastic Collisions
27 CollisionsThe total momentum remains constant in any type of collision. However, the total kinetic energy is generally not conserved in a collision because some kinetic energy is converted to internal energy when the objects deform.
28 Several Types of collisions Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved.When 2 objects collide and DON’T stickWhen 2 objects collide and stick togetherWhen 1 object breaks into 2 objectsElastic Collision = Kinetic Energy is ConservedInelastic Collision = Kinetic Energy is NOT ConservedPerfectly Inelastic = Momentum is conserved kinetic energy is not, & two objects stick together. Vf = same.
29 Perfectly Inelastic Collisions When two objects, such as the two football players, collide and move together as one mass, the collision is called aPerfectly Inelastic CollisionVf = ? The final velocity isthe same for both playersThe final velocity is the same for both players
30 Pause for a CauseA 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?Given:m1 = 1850 kgm2 = 975 kgv1,i = 0 m/sv2,i = 22.0 m/s to the northUnknown:vf = ?Practice E
31 Pause for a CauseA diver with a mass of 80.0 kg jumps from a dock into a kg boat at rest on the west side of the dock. If the velocity of the diver in the air is m/s to the west, what is the final velocity of the diver after landing in the boat?Practice E
32 Kinetic Energy & Perfectly Inelastic Collisions In an inelastic collision, the total kinetic energy does not remain constant when the objects collide and stick together.EQ: Where does some of the energy go?sound energy & internal energy as the objects deform during the collision.The decrease in the total kinetic energy during an inelastic collision can be calculated by using the formula for kinetic energy.It is important to remember that not all of the initial kinetic energy is necessarily lost in a perfectly inelastic collision.
33 Pause for a CauseAn infant throws 5 g of applesauce at a velocity of 0.2 m/s. All of the applesauce collides with a nearby wall and sticks to it. What is the decrease in kinetic energy of the applesauce?
34 Pause for a Cause ΔKE = KEf − KEi Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision?Given:m1 = kgm2 = kgv1,i = 4.00 m/s to the right,v1,i = m/sv2,i = 3.00 m/s to the left,v2,i = −3.00 m/sUnknown:ΔKE = ?ΔKE = KEf − KEi
35 Pause for a Cause ΔKE = KEf − KEi Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision?ΔKE = KEf − KEiUnknown:ΔKE = ?Practice F
36 Pause for a Cause -ΔKE = KEf − KEi Two snowballs with masses of 0.40 kg and 0.60 kg, respectively, collide head-on and combine to form a single snowball. The initial speed for each is 15 m/s. If the velocity of the new combined snowball is 3.0 m/s after the collision, what is the decrease in kinetic energy?-ΔKE = KEf − KEiPractice F
37 Elastic CollisionsIn an elastic collision two objects collide and return to their original shapes with no loss of total kinetic energy. After the collision, the two objects move separately. In an elastic collision, both the total momentum and the total kinetic energy are conserved.Perfectly inelastic collisions rarely happen in the real world.Most collision are not elastic either. Some kinetic energy is lost.Ex: Collision Football & FootBoth are deformed and loss energy to sound.Any collision that makes sound can not by definition by elasticEX: the click of billiard balls.**Remember that v is positive if the object moves to the right and negative if the object moves to the left**
38 **Remember that v is positive if the object moves to the right and negative if the object moves to the left**
39 Pause for a CauseA kg marble moving to the right at m/s makes an elastic headon collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface. What is the velocity of the kg marble after the collision?Given:m1 = kgm2 = kgv1,i = m/s to the right,v1,i = m/sv2,i = m/s to the left,v2,i = −0.180 m/sv1,f = m/s to the left,v1,f = −0.315 m/sUnknown:v2,f = ?= 9.0 x 10-2 m/s to the right= 9.0 x 10-2 m/s to the right
40 Pause for a Cause Calculate the final KE and the initial KE. Practice G