Phys 101, Sp 15 HW Chpt 9: Linear Momentum Name ________________ 1) State Newton's second law of motion in terms of momentum. 2) State the Law of Conservation of Linear Momentum. 3) Is it realistic to apply the conservation of momentum to real world collisions where external forces act? 4) A novice marksman fires a rifle while holding the butt of the rifle a couple of centimeters away from his shoulder. Explain what happens in terms of the physical principles involved. 5) Define an inelastic collision in terms of conservation of momentum and energy. 6) Define an elastic collision in terms of conservation of momentum and energy. 7) Explain the process through which kinetic energy is conserved in an elastic collision. 8) When a ball undergoes a one-dimensional elastic collision with a wall, the velocity of the ball is reversed, while the wall remains stationary. Explain why this does not violate conservation of momentum. 9) Explain the process through which kinetic energy is lost in an inelastic collision. 10) Is it possible for kinetic energy to increase during an inelastic collision? Explain. 11) When a ball undergoes a two-dimensional elastic collision with a smooth wall, the angle that the incident path makes with the perpendicular to the wall is equal to the angle that the outgoing path makes with the perpendicular to the wall. Explain why this is so. 12) In the two-dimensional elastic collision of a particle with a stationary particle that has the same mass, the trajectories of the two particles after the collision are at right angles to each other. Explain why this should be so. 13) In space there is nothing for the rocket to "push against" so how does it accelerate? 14) The net force acting on an object is equal to the rate of change of its momentum. 15) The change in the momentum vector is in the direction of the net force. 16) The impulse delivered to an object is equal to the change in the object's velocity. 17) Collisions in which kinetic energy is conserved are said to be ineleatic collisions. 18) Collisions in which total energy is conserved are said to be elastic collisions. 19) In a one-dimensional elastic collision of two identical masses, the masses always exchange velocities. 1 20) In any elastic head-on collision, the relative speed of the two objects after the collision has the same magnitude (but opposite direction) as before the collision, no matter what the masses are. 21) In an inelastic collision, the total kinetic energy after the interaction can be greater than the initial kinetic energy. 22) The center of mass of a system of particles (or objects) with total mass M moves like a single particle of mass M acted upon by the same net external force. 23) The linear momentum of an extended object is the product of the object's mass and the velocity of its center of mass. 24) An interacting system of two objects has no external force acting on the system. The first object has a mass 2.00 kg and is moving with a velocity (2.00 m/s)i^+ (1.00 m/s)j^at time t = 0.00 s. The second object has a mass 3.00 kg and is moving with a velocity (-1.00 m/s)i^+ (1.00 m/s)j^ at time t = 0.00 s. The second object is moving with a velocity (2.00 m/s)i^+ (-1.00 m/s)j^at time t = 1.00 s. (a) What is the total momentum of the system at time t = 0.00 s? (b) What is the velocity of the first object at t = 1.00 s? 25) A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. (a) What is the speed of the wreckage just after the collision? (b) In what direction does the wreckage move just after the collision? 26) A long thin rod of length L has a linear density λ(x) = Ax where x is the distance from the left end of the rod. (a) How far is the center of mass of the rod from the left end of the rod? (b) What is the mass of the rod? 27) A long thin rod of length L has a linear density λ(x) = A(L -x)2 where x is the distance from the left end of the rod. (a) How far is the center of mass of the rod from the left end of the rod? (b) What is the mass of the rod? 28) A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground. It rebounds with a speed of 1.00 m/s. What is the change of the ball's momentum? 29) A firecracker breaks up into two pieces, one has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s and the second has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces? 30) Two objects are moving in the xy-plane. Object A has a mass of 3.2 kg and has a velocity v A = (2.3 m/s)i^+ (4.2 m/s)j^and object B has a mass of 2.9 kg and has a velocity v B = (-1.8 m/s)i^+ (2.7 m/s)j^. What is the total momentum of the system? 2 31) Two objects are moving in the xy-plane. Object A has a mass of 3.5 kg and has a velocity v A of 5.3 m/s at an angle of 30° from the x-axis and object B has a mass of 1.9 kg and has a velocity v B of 6.2 m/s at an angle of 72° from the x-axis. What is the total momentum of the system? 32) A 0.250-kg rubber ball is dropped from a height of 2.00 m. It hits the floor and rebounds to a height of 1.80 m. What is the magnitude of impulse the floor applies to the ball? 33) During a collision with a wall, the velocity of a 0.200-kg ball changes from 20.0 m/s toward the wall to 12.0 m/s away from the wall. If the time the ball was in contact with the wall was 60.0 ms, what was the magnitude of the average force applied to the ball? 34) A 1000-kg car is traveling at 20.0 m/s toward the north. During a collision the car receives an impulse of 1.00 × 10 4 N∙s toward the south. What is the velocity of the car after the impulse is applied to the car? 35) Two ice skaters push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s. What speed does the 60-kg skater acquire? 36) A 0.400-kg ball approaches a very massive wall at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy. What is the magnitude of the change in momentum of the wall? 37) A 3.00-kg object traveling 20.0 m/s west collides with a 5.00-kg mass object traveling 12.0 m/s west. The collision is perfectly elastic, what is the velocity of the 3.00-kg object after the collision? 38) A 1000-kg car is traveling north at 20.0 m/s. A 1500-kg car is traveling north at 36.0 m/s. The 1500-kg collides with the rear of the 1000-kg car and they lock together. Ignoring external forces acting during the collision, what is the velocity of the cars immediately after the collision? 39) Three masses are located in the x-y plane as follows: a mass of 6 kg is located at (0 m, 0 m), a mass of 4 kg is located at (3 m, 0 m), and a mass of 2 kg is located at (0 m, 3 m). Where is the center of mass of the system? 40) A uniform piece of wire, 20 cm long, is bent in a right angle in the center to give it an L-shape. How far from the bend is the center of mass of the bent wire? 41) A 2.00-kg mass is located at (4.00 m)i^+(-1.00 m)j^. A 1.00-kg mass is located at (1.00 m)i^+ (2.00 m)j^. Where must a 3.00-kg mass be located so that the center of mass of the system is located at (-1.00 m)i^+ (1.00 m)j^? 3

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