Physics in Action Soccer players must consider an enormous amount of information every time they set the ball = or themselves into motion. Once a player knows where the ball should go, the player has to decide how to get it there. The player also has to consider the ball s speed and direction. The player in the photograph must determine how much follow-through is needed. To do this, she must understand her own motion as well as the motion of the ball. International regulations specify the mass of official soccer balls. How does the mass of a ball affect the way it behaves when kicked? How does the velocity of the player s foot affect the final velocity of the ball?
Questions: Is the pin more likely to move rapidly when the ball travels at a high speed or at a low speed? If two bowling balls of different masses move at the same speed, which is more likely to move the pin?
Momentum and Impulse
Momentum Momentum describes an object s motion In physics momentum is represented by the symbol p Linear momentum of an object of mass m moving with a velocity v is defined as p = mv Momentum = mass x velocity
Momentum Momentum is a vector quantity whose direction matches that of the velocity SI Unit: kilogram meters per second (kgm/s)
Practice Problems A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck? p = 5.6 x 10 4 kg m/s to the east A 21 kg child is riding a 5.9 kg bike with a velocity of 4.5 m/s to the northwest. What is the momentum of the child and the bike together? 1.2 x 10 2 kg m/s to the northwest What is the momentum of the child? 94 kg m/s to the northwest What is the momentum of the bike? 27 kg m/s to the northwest
Changing Momentum A change in momentum takes a force Sir Isaac Newton Impulse-Momentum Theorem F t is called the impulse of the force F for the time interval t
Practice A 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 magnitude of the force exerted on the car during the collision. 7.0 x 10 4 N to the east An 82 kg man drops from rest on a diving board 3.0 above the surface of the water and comes to rest 0.55 s after reaching the water. What force does the water exert on him? 1.1 x 103 N upward
Stopping Times and Distances Impulse-momentum theorem can be used to determine stopping distances and safe following distances for cars and trucks Stopping time can be found by reorganizing the impulse momentum theorem Stopping distance is found by using the displacement formula ( x =1/2(v f +v i ) t)
Practice A 2250 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 8450 N to the east? How far does the car travel during the deceleration? t = 4 seconds 50.0 m = 50.0 m to the west
Increasing Momentum To increase the momentum of an object, it makes sense to apply the greatest force possible for as long as possible Examples: A golfer teeing off A baseball player trying for a home run Some forces cause a distortion to the object
Decreasing Momentum Here s some common sense thinking If you were in a car that was out of control and you had to choose between hitting a concrete wall or a hay stack which would you choose?
Review The speed of a particle is doubled. By what factor is its momentum changed? Momentum increases by a factor of two What happens to it s kinetic energy? Kinetic energy increases by a factor of four When a force is exerted on an object, does a large force always produce a larger change in the object s momentum than a smaller force does? No; because p=f t, it is possible for a large force applied over a very short time interval to change the momentum less than a smaller force applied over a longer time period
Conservation of Momentum
Momentum is Conserved Before a collision the momentum of ball B is zero During the collision, ball B gains momentum and ball A looses momentum The amount of momentum lost by ball A is equal to the amount of momentum gained by ball B The TOTAL momentum of the two balls together remains constant
Conservation of Momentum The momentum of ball B before the collision is equal to the momentum of ball A plus the momentum of ball B after the collision. P a,i + P b,i = P a,f + P b,f Law of Conservation of Momentum m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f Total initial momentum = total final momentum
Is It Only Collisions? Total momentum remains constant for a system of objects that interact with one another
Practice 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? 4.2 m/s to the left
Practice A 63.0 kg astronaut is on a spacewalk when the tether line to the shuttle breaks. The astronaut is able to throw a 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 12.0 m/s, propelling the astronaut back to the shuttle. Assuming that the astronaut starts from rest, find the final speed of the astronaut after throwing the tank. 1.90 m/s
Collisions Three types of collisions: Perfectly inelastic collisions Inelastic collisions Elastic collisions
Perfectly Inelastic Collisions Two objects collide and move together as one mass The two objects essentially become one object after the collision Conservation of momentum m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f Kinetic energy is NOT constant in inelastic collisions
Inelastic Collision The colliding objects bounce and move separately after the collision, but the total kinetic energy decreases due to deformation of the object We will not consider these types of problems in this class
Elastic Collision Two objects collide and return to their original shape with no change in total kinetic energy After the collision the two objects move separately The total momentum and total kinetic energy remain constant (conserved)
Practice A 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? V f = 7.59 m/s to the north
Practice Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The mass of the second ball is 0.250 kg, and it has an initial velocity of 3.00 m/s to the left. What is the final velocity of the composite ball of class after the collision? What is the decrease in kinetic energy during the collision? Vf = 1.67 m/s to the right KE = -4.07 J
Practice A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on collision with a 0.030 kg shooter marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 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 0.0309 kg marble after the collision? 0.090 m/s to the right