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ic_sol_w09d1_1

# ic_sol_w09d1_1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 TEAL Fall Term 2004 In-Class Problems 27-29: Momentum and Collisions: Solutions Problem 27: Elastic One Dimensional Collision Consider the elastic collision of two carts along a track; the incident cart 1 has mass m 1 and moves with initial velocity v 1,0 . The target cart has mass m 2 = 2 m and is initially at rest 1 v 2,0 = 0 . Immediately after the collision, the target cart has final speed v 1, f and the target cart has final speed v 2, f . Calculate the final velocities of the carts as a function of the initial velocity v 1,0 . Solution a) Draw a momentum diagram. Figure 10.11 Momentum flow for a one-dimensional collision. b) Find the equation for conservation of momentum in the lab reference frame. m v = − m v + 2 m v 2, f . 1 1,0 1 1, f 1 Thus v 1,0 = − v 1, f + 2 v 2, f . c) Find the equation for conservation of energy in the lab reference frame. 1 m v 2 = 1 m v 1 . 2 1 1,0 2 1 1, f 2 + 1 2 2 m v 2, f 2 Thus 1

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2 2 v 1,0 = v 1, f + 2 v 2, f 2 .
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ic_sol_w09d1_1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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