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Schaum's Chapter 8 Momentum

Schaum's Chapter 8 Momentum 8.1 An 8 g bullet is fired horizontally into a 9 kg cube of wood, which is at rest, and sticks in it. The cube is free to move and has a speed of 40 cm/s after impact. Find the initial velocity of the bullet. 450.4 m/s

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Schaum's Chapter 8 Momentum

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  1. Schaum's Chapter 8 Momentum 8.1 An 8 g bullet is fired horizontally into a 9 kg cube of wood, which is at rest, and sticks in it. The cube is free to move and has a speed of 40 cm/s after impact. Find the initial velocity of the bullet. 450.4 m/s 8.2 A 16 g mass is moving in the +x direction at 30 cm/s while a 4 g mass is moving in the -x direction at 50 cm/s. They collide head on and stick together. Find their velocity after the collision. .14 m/s Before = After m1v1 + m2v2 = (m1 + m2)v1 0.008v + 0 = (0.008 + 9)v v = 450.4 m/s Before = After m1v1 + m2v2 = (m1 + m2)v1 0.016(.3) + (0.004)(-0.5) = (0.016 + 0.004)v v = 0.14 m/s 8.3 A 2 kg brick is moving at a speed of 6 m/s. How large a force F is needed to stop the brick in a time of 7 x 10-4 s? 8.4 A 15 g bullet moving at 300 m/s passes through a 2 cm thick sheet of foam plastic and emerges with a speed of 90 m/s. What average force impeded the bullet's motion through the plastic? FΔT = mv F(7X10-4) = 2(0-6) F = -17142.86 N OPPOSES MOTION STOPS - 17.14 kN Assume constant acceleration x = vt .02 = ( 300 + 90 ) t t = 1.026 x 10-4 sec 2 FΔT = mv F(1.026X10-4) = .015(90-300) F = -30701.75 N OPPOSES MOTION STOPS -30.7 kN

  2. 8.5 The nucleus of an atom has a mass of 3.80 x 10-25 kg and is at rest. The nucleus is radioactive and suddenly ejects a particle of mass 6.6 x 10-27 kg and speed 1.5 x 107 m/s. Find the recoil speed of the nucleus that is left behind. 265.42 km/s 8.6 A 0.25 kg ball moving in the +x direction at 13 m/s is hit by a bat. Its final velocity is 19 m/s in the - x direction. The bat acts on the ball for 0.010 s. Find the average force F exerted on the ball by the bat. - 800 N Before = After m1v1 + m2v2 = m1v11 + m2v21 0 = (3.8 x 10-25 - 6.6 x 10 -27)v + 6.6 x 10 -27 (1.5 x 107) v = 265415.55 m/s FΔT = mv F(0.01) = .25(-19-13) F = -800 N OPPOSITE ORIGINAL DIRECTION +13 -19 8.21 Typically, a tennis ball hit during a serve travels away at about 51 m/s. If the ball is at rest mid air when struck, and it has a mass of 0.058 kg, what is the change in its momentum leaving the racket? 2.96 kg m /s 8.22 During a soccer game a ball (of mass 0.425 kg) which is initially at rest is kicked by one of the players. The ball moves off at a speed of 26 m/s. Given that the impact lasted for 8 ms, what was the average force exerted on the ball? 1.38 kN ΔP = mv ΔP= .058(51) ΔP = 2.96 kgm s FΔT = mv F(0.008) = .425(26) F = 1381.25 N

  3. 8.23 A 40000 kg freight car is coasting at a speed of 5 m/s along a straight track whenit strikes a 30000 kg stationary freight car and couples to it. What will be their combined speed after impact? Before = After m1v1 + m2v2 = m1v11 + m2v21 40000(5) = (40000 + 30000)v v = 2.86 m/s 8.24 An empty 15000 kg coal car is coasting on a level track at 5 m/s. Suddenly 5000 kg of coal is dumped into it from directly above it. The coal initially has zero horizontal velocity. Find the final speed of the car. 8.25 Sand drops at a rate of 2000 kg/min from the bottom of a stationary hopper onto a belt conveyer moving horizontally at 250 m/min. Determine the force needed to drive the conveyor, neglecting friction. Before = After m1v1 + m2v2 = m1v11 + m2v21 15000(5) = (15000 + 5000)v v = 3.75 m/s 2000 kg/ min (1min/60 sec) = 33.33 kg/ sec 250 m/min ( 1 min/60 sec) = 4.17 m/sec FΔT = mv F = mv N = kg m F = kg m F = 33.33 kg ( 4.17 m ) ΔT s2 (s)(s) s s F = 138.99 N

  4. 10cm v1 8.8 As shown in the figure, a 15 g bullet is fired horizontally into a 3000kg block of wood suspended by a cord. The bullet sticks in the block. Compute the speed of the bullet if the impact causes the block to swing 10 cm above its initial level. 8.13 Two balls of equal mass approach the coordinate origin, one moving downward along the +y axis at 2 m/s and the other moving to the right along the -x axis at 3 m/s. After they collide, one ball moves out to the right along the +x axis at 1.2m/s. Find the scalar x and y components of the other ball. Before = After m1v1 + m2v2 = m1v11 + m2v21 ΔPE = ΔKE .015 v = 3.015 (1.4) v = 281.40 m/s 1/2 mv2 = mgh 1/2 v2 = 9.8 (.10) v = 1.4 m/s .015v = 3.015v1 + y direction m(2) = mvy vy = 2 m/s The other ball moves right and down x direction m(3) = m(1.2) + mvx vx = 1.8 m/s + 8.14 A 7500 kg truck traveling at 5 m/s east collides with a 1500 kg car moving at 20 m/s in a direction 300 sw. After the collision, the two vehicles remain tangled together. With what speed and in what direction does the wreckage begin to move? 20 cos 30 = 17.32 30 20 sin 30 = 10

  5. 8.26 Two bodies of masses 8 kg and 4 kg move along the x axis in opposite directions with velocities of 11 m/s positive x direction and 7 m/s negative x direction respectively. They collide and stick together. Find their velocity just after the collision. 8.27 A 1200 kg gun mounted on wheels shoots an 8 kg projectile with a muzzle velocity of 600 m/s at an angle of 300 above the horizontal. Find the horizontal recoil speed of the gun. 8.15 Two identical balls collide head on. The initial velocity of one is 0.75 m/s east while that of the other is 0.43 m/s west. If the collision is perfectly elastic, what is the final velocity of each ball?

  6. 8.32 A 2 kg block of wood rests on a long table top. A 5 g bullet moving horizontally with a speed of 150 m/s is shot into the block and sticks in it. The block then slides 270 cm along the table and stops. a) Find the speed of the block just after impact. b) Find the friction force between block and table. Ff = ma Ff = 2(.025) Ff = 0.05 N vf2 = v02 + 2ax 0 = .372 + 2a(2.7) a = 0.025 m/s2 .005(150) + 0 = 2.005 v v = 0.37 m/s 8.33 A 2 kg block of wood rests on a table top. A 7 g bullet is shot straight up through a hole in the table beneath the block. The bullet lodges in the block and the block flies 25 cm above the table top. Initial spped of bullet? 8.34 A 6000 kg truck traveling north at 5 m/s collides with a 4000 kg truck moving west at 15 m/s. If the two trucks remain locked together after the impact with what speed and in what direction do they move? ,007 v1 = 2.007 (2.21) v1 = 633.64 m/s ΔKE = ΔPE 1/2 (v11)2 = 9.8(.25) v11 = 2.21 m.s mblock = 2 kg v1 = 0 mbullet = .007 kg v1 = ? 4000 (15) = 10000 vx vx = 6 m/s West 6000 (5) = 10000 vy vy = 3 m/s North

  7. + + 8.35 What average resisting force must act on a 3 kg mass to reduce its speed from 65cm/s to 15 cm/s in 0.20 s? FΔt = mΔv F(.20) = 3(.65-.15) F = 7.5N 8.36 A 7 g bullet moving horizontally at 200 m/s strikes and passes through a 150 g tin can sitting on a post. Just after impact the can has a horizontal speed of 180 cm/s. What was the bullets speed after leaving the can? Before = After .007(200) = .007v + .15(1.8) 1.4 = .007v + .27 v = 161.43 m/s 8.37 Two balls of equal mass moving with speeds of 3 m/s collide head-on. Find the speed of each after impact if the collision is perfectly elastic. m1 = m2 can leave out of equation head on one positive and one negative v1 + v2 = v11 + v21 3-3 = v11 + v21 0 = v11 + v21 v11 = - 3 v1 - v2 = v21 - v11 v21 v21 - v11 3-(-3) = 6 = = 3 v21 - v11

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