PHY-102: Energy and Circular Motion Exercises

PHY-102: Energy and Circular Motion Exercises Complete the following exercises. 1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel. a. Explain this using the impulse-momentum theorem. By the theory of momentum, change in momentum of an object equals the impulse applied to it meaning that the long barrel of the rifle covers a huge amount of motion of the bullet since the bullet receives more impulse from the expanding gases with an inch of length of the barrel compared to the short rifle. b. Explain this using the work-energy theorem By work-energy theorem, the work done by all forces acting a particle equals the change in the particle’s kinetic energy meaning that the discharge of the bullet caused is slower but has more power than the one with the short barrel. 2. Use physics terms to explain the benefits of crumple zones in modern cars. A crump zone is intended to slow down the crash, and also absorb energy to reduce the difference between the speed of the car occupants; traveling at speed due to momentum, and the car (abruptly stopped). 3. When a gun is fired at the shooting range, the gun recoils (moves backward). Explain this using the law of conservation of momentum. According to the law of conservation of momentum, the total momentum is unchanged. Hence, when the gun is fired, the bullets gain a high velocity forward that is positive velocity and that velocity multiplied by its mass equals the momentum gained. Therefore, the gun must gain a momentum backward to cancel out the forward momentum, so the gun recoils back with negative velocity. 4. Rank the following in terms of increasing inertia: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s DBCA (inertia is a component of mass) 5. Rank the following in terms of increasing momentum: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s ABDC (momentum=mv) 6. Rank the following in terms of increasing kinetic energy: A. A 1200 kg car going 15 m/s B. A 10,000 kg train car at rest C. A 15 kg meteor going at a speed of 1000 m/s D. A 100 kg person running at 5 m/s BDAC (kinetic energy=0.5*m*v2 ) 7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision.Findthe speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s.Describe the work you did to get the answer. V=2.5m/s Since Ben was standing his initial momentum is 0. After collision they embrace and hence will have a common velocity. By law of conservation of momentum: initial momentum = final momentum Therefore, MJ VJ=(MB+MJ )V (25)(8)=(55+25)V V=200 /80=2.5m/s 8. Identical marblesare released from the same height on each of the following four frictionless ramps. Compare the speed of the marbles at the end of each ramp. Explain your reasoning. The speed of the marbles will highest at D followed by A then B and lowest speed would in C. For ramp D the incline is steep at the beginning hence the average speed will be higher allowing the ball to arrive fastest. For ramp A the inclination is steeper at the beginning compared to B and C and since the incline is uniform hence the speed will be higher compared to B and C. For ramp B the incline is not steep at the beginning but becomes steeper towards the end hence the speed will be higher compared to C. For ramp C though the speed will be high the curving at the end reduces the ball’s speed drastically