HW 6Solutions

HW 6Solutions - 1) Three identical train cars, coupled...

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Unformatted text preview: 1) Three identical train cars, coupled together, are rolling east at 2.0 m/s. A fourth car traveling east at 4.0 m/s catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train? 9.32. Model: Model the train cars as particles. Since the train cars stick together, we are dealing with perfectly inelastic collisions. Momentum is conserved in the collisions of this problem. Visualize: Solve: In the collision between the three-car train and the single car: mv 1x + (3m )v 2x = 4mv 3 x fi v1 x + 3v2x = 4v3x fi (4.0 m/ s) + 3(2.0 m/ s) = 4v 3 x fi v3x = 2.5 m / s In the collision between the four-car train and the stationary car: ( 4m )v3 x + m v4 x = (5m )v5 x fi 4v3 x + 0 m /s = 5v5x fi v5 x = 4v3x 5 = ( 0.8 )( 2.5 m /s ) = 2.0 m /s 2) A 1000 kg cart is rolling to the right at 5.0 m/s. A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of 10 m/s relative to the cart? 9.67. Model: The cart+man (C+M) is our system. It is an isolated system, and momentum is conserved. Visualize: Solve: The conservation of momentum equation pfx = pix is m M ( vfx )M + m C (v fx ) C = m M ( vi x ) M + m C ( vi x )C Note that (vf)M and (vfx)C are the final velocities of the man and the cart relative to the ground. What is given in this problem is the velocity of the man relative to the moving cart. The man's velocity relative to the ground is (v ) fx M = ( vfx )C - 10 m / s With this form for (vfx)M, we rewrite the momentum conservation equation as [ fi (70 kg )[( v m M ( vfx )C - 10 m / s + m C ( vfx )C = m M (5 m / s ) + m C (5 m / s ) fx ) C - 10 m / s] + (1000 kg )(v fx ) C = (1000 kg + 70 kg )(5 m / s ) fi (vfx ) C [1000 kg + 70 kg ] = (1070 kg )(5 m / s ) + (70 kg )(10 m / s ) fi (vfx ) C = 5.65 m / s ...
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This note was uploaded on 05/20/2008 for the course PHYS 161 taught by Professor Hammer during the Spring '07 term at Maryland.

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