Preliminary Work 1. A 2 kg bouncy ball is dropped from a height of 10 m, hits the floor and returns to its original height. What was the change in momentum of the ball upon impact with the floor? What was the impulse provided by the floor? [ Answer: 56 Ns; 56 Ns ] 2. A ball of 2 kg is thrown straight up into the air with an initial velocity of 10 m/s. What was the total change in its momentum just before the ball lands? Using the impulse-momentum theorem, calculate the time of flight of the ball. Confirm the time using kinematics. [ Answer: 40 Ns; 2 s ] 3. According to the Guinness Book of World Records, the fastest recorded cricket ball was bowled by Shoaib Akhtar. The pitch was clocked at 161.4 km/hr. Determine the impulse required to give a 0.163 kg ball such a momentum. [ Answer: 7.13 Ns ] 4. Kare Less was applying her makeup when she drove into Chadstone s busy parking lot last Friday morning. Unaware that there was bus stopped in her lane 98.5 m ahead, Kara rear-ended the bus. Kare s 1300 kg car was moving at 11 m/s and stopped in 0.14 s. (a) Determine the momentum change of Kare s car. (b) Determine the impulse experienced by Kare s car. (c) Determine the magnitude of the force experienced by Kare s car. [ Answer: a) -1.4 10 4 kgm/s; b) -1.4 10 4 Ns; c) 1.0 10 5 N ] 5. While playing basketball in PE class, Logan lost his balance and collided with the padded wall behind the basket. His 74 kg body decelerated from 7.6 m/s to 0 m/s in 0.16 s. Determine the force acting upon Logan s body. If Logan had hit the concrete wall moving at the same speed, his momentum would have been reduced to zero in 8 ms. Determine what the force on his body would have been for such an abrupt collision. [ Answer: 3.5 10 3 N; 7.0 10 4 N ] 6. A FSP student was practising her tennis strokes in front of a concrete wall. The 57.5 g ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331 g racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s. (a) Determine the pre-collision momentum of the ball. (b) Determine the post-collision momentum of the ball. (c) Determine the momentum change of the ball. (d) Determine the velocity change of the racket. [ Answer: a) 1.5 kgm/s, North; b) 1.70 kgm/s, South; c) 3.23 kgm/s, South; d) 9.76 m/s, North ] 1
Tute M9 : CONSERVATION OF MOMENTUM 1 Momentum p = mv Impulse I = F t 1. A toy train with mass M = 0.42 kg moving with velocity v t = 0.3 m s 1 to the right hits a carriage of mass m = 0.2 kg moving at v c = 0.32 m s 1 in the opposite direction. If they stick together, what is their common velocity v after the collision? [ Answer: v = 0.1 ms 1 to the right ] [Find the total kinetic energy before and after the collision to determine whether the collision was elastic or inelastic.] [ Answer: Inelastic collision ] 2. A mass M = 5 kg moving with a velocity U = 2 m s 1 has an elastic collision with a stationary mass m = 1 kg. Calculate the final velocities V and v of both masses after the collision. Ensure that you properly explain the physical principles upon which you base your solution. [ Answer: V = 4 3 m s 1 and v = 10 3 m s 1 ] 3. Two metal spheres of masses m and 2m are hung side by side so that they just touch at point B as shown below. The smaller mass m is drawn aside to point A which is a height h above B and then released so that it makes an elastic collision with the 2m mass. 1 June 4, 2014 2
(a) What is the velocity u of mass m just before the collision? (b) Using the appropriate conservation laws, find expressions for the velocities of m and 2m (v and V respectively) just after the collision. [ Answer: (a) u = 2gh ; (b) v = 1 3 2gh V = 2 3 2gh ] 4. Four identical ball bearings, each of mass m, lie in contact in a straight line. A fifth ball bearing travelling with velocity v makes an in-line elastic collision with the other four. Prove that, in this case, one (and only one) ball bearing will be ejected from the other end. [ Answer: Proof will be given in the physics tutorial. ] 5. A Ford Capri with mass m = 1,100 kg is travelling at 30 m s 1 on a freeway. A MACK truck with mass M = 20,000 kg is moving with the same speed in the opposite direction. A faulty wheel bearing on the Capri causes it to swerve onto the wrong side of the freeway and have a head-on collision with the truck. If the two vehicles stick together on impact, what is the velocity of the composite system after the collision? Is the collision elastic? [ Answer: v f = 26.9 m s 1 in the initial direction of motion of the MACK truck ; No, since kinetic energy is not conserved. ] 6. A white billiard ball moving along the x axis at 5 m s 1 hits a stationary red billiard ball. After the collision the white ball moves with a speed of 4 m s 1 at an angle of 30 above the x axis and the red ball has a speed v f at an angle θ below the x axis. Determine v f and θ for the red billiard ball. [ Answer: v f = 2.5 ms 1 and θ = 52.5 ] 3
7. A professional ten pin bowler throws a 5.5 kg bowling ball with a velocity of 6 m s 1 towards a single, stationary bowling pin. The bowling ball makes a head-on collision with the 1.6 kg pin and continues to roll forward with a velocity of 4 m s 1. (a) Find the velocity of the pin just after the collision. (b) Is this collision elastic? [ Answer: (a) v p = 6.9 m s 1 (b) No, kinetic energy isn t conserved. ] 8. Two sumo wrestlers by the names of Fatsono and Frankimoto charge towards each other with speeds of 4.5 m s 1 and 6.5 m s 1 respectively. Fatsono has a mass of 180 kg and Frankimoto a mass of 100 kg. They make an in-line collision. If they hold on to each other once they collide, what is the final velocity of the composite mass and in which direction will they travel? Is this collision elastic? [ Answer: The final velocity is 0.57 m s 1 in the Fatsono direction. The collision is inelastic as kinetic energy is not conserved. ] 9. The head of a golf club with a mass of 0.25 kg is moving with a speed of 55 m s 1 just before striking a stationary 50 g golf ball. After the collision, the golf club continues to move (in the same direction) but with a reduced speed of 40 m s 1. Use conservation of momentum to find the speed of the golf ball and determine whether or not the collision was elastic. [ Answer: v = 75 m s 1 ; The collision was inelastic. ] 10. An unstable (stationary) nucleus with a mass of 1.70 10 26 kg disintegrates into three particles. One particle with a mass of 5.0 10 27 kg moves in the y direction with a speed of 6.0 10 6 m s 1. A second particle with a larger mass of 8.4 10 27 kg moves in the x direction with a speed of 4 10 6 m s 1. Find the velocity and speed of the third particle emitted in this decay. [ Answer: V = 9.33 10 6 i 8.33 10 6 j m s 1 ; V = 1.25 10 7 m s 1 ] 4
Further Practice Problems: 1. Slim Jim is choosing to jump onto a trampoline or a wood block from a height of 10 m. Both the trampoline and wood block are 2 m high. In which case will he have the most momentum before hitting? In which case will feel the most force? In which case will he take more time to stop? In which case will he feel the greatest impulse? [ Answer: same ; wood ; trampoline ; same ] 2. Which of the following equations answer the following questions the best. Note: p1+p2 means the combine momentum of objects 1 and 2, B means Before and A means After. Two objects at rest push off from each other. Two people in moving bumper cars collide and bounce off. A skateboarder is moving and throws something. A person pushes on a car that is already rolling. A football player catches a football. Two moving objects collide, stick together, and stop. (a) pb + I = pa (b) p1b + p2b = p1a + p2a (c) p1b + p2b = p1 + 2A (d) p1 + 2B = p1a + p2a (e) p1b + p2b = 0 (f) 0 = p1a + p2a 3. A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a) What is the impulse delivered to the ball by the racquet? (b) What work does the racquet do on the ball? [ Answer: -5.4 kgm/s ; -27 J ] 5
Further Interesting Problems: 1. Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. A cord initially holding the blocks together is burned; after this happens, the block of mass 3M moves to the right with a speed of 2.00 m/s. (a) What is the velocity of the block of mass M? (b) What is the systems original elastic potential energy in the spring if M = 0.350 kg. (c) Is the original energy in the spring or in the cord? Explain your answer. [ Answer: 6 m/s in the -x direction ; 8.4 J ; spring ] 2. Slim Jim throws a 1 kg ball at the ground from a height of 0.5 m with a velocity of 6 m/s and at an angle 70 to the vertical. The ball then bounces from the ground and lands on the ground at distance x from its first bounce. 30% of its energy is lost in the first bounce. What is the change in the momentum of the ball? What is the velocity of the ball after its first bounce? Find the range of the ball. (How far away it lands.) [ Answer: 11.7 kgm/s ; 5.67m/s ; 2.78 m ] 3. An 85 kg lumberjack stands at one end of a 380 kg floating log, as shown. Both the log and the lumberjack are at rest initially. If the lumberjack now trots toward the other end of the log with a speed of 2.7 m/s relative to the log, what is the lumberjacks speed relative to the shore? [ Answer: 2.21 m/s ] 4. A 57.0 kg person holding two 0.850 kg bricks stands on a 2.10 kg skateboard. Initially, the skateboard and the person are at rest. The person now throws the two bricks at the same time so that their speed relative to the person is 18.0 m/s. What is the recoil speed of the person and the skateboard relative to the ground, assuming the skateboard moves without friction? [ Answer: 0.503 m/s ] 6
5. A smooth sphere A, of mass 2 kg and moving with speed 6 m/s collides obliquely with a smooth sphere B of mass 4 kg. Just before impact B is stationary and the velocity of A makes an angle of 60 with the lines of centres of the spheres. If B moves of with a speed of 1.25 m/s along the line of centres, find the velocity of A after the impact. [ Answer: 0.5i - 5.196j m/s ] 6. A block of mass m rests on a wedge of mass M which in turn rests on a horizontal table. All the surfaces are smooth and the system is initially at rest. Find the velocity of the wedge when the block m after sliding down, just touches the ground. [ Answer: 2m 2 g cos 2 θh (M+m)(M+m sin 2 θ) ] 7. A ball of mass m 1 = 0.2 kg hits a second mass m 2 at a speed of u = 2 m/s. m 2 initially is located in the middle of the table. After the collision, m 2 is projected off the table top at a speed of v 2 and lands a distance of d from the table edge. m 1 travels back the same way it came from, and is then projected off the table and lands a distance of 4d. Assume no energy is lost during the entire collision and journey. Find m 2 and v 2. u m2 [ Answer: 1.8 kg ; 0.4 m/s ] m1 before after 4d d 7