A 500 gram dynamics cart starts at rest and rolls down a track thatis 2.5 meters

Question

A 500 gram dynamics cart starts at rest and rolls down a track thatis 2.5 meters long and elevated 15 cm on one end. At thebottom of the track it rolls onto a level surface and then collideswith a 1200 g cart that is sitting still. The collision isperfectly inelastic.

1. Calculate the kinetic energy that was lost in the collision.(0.52 J)
2. Determine the momentum lost in the collision (0.0 kgm/s)

Please show all work, in order to receive a rating of Lifesaver!Thank you so much! :) Calculate the kinetic energy that was lost in the collision.(0.52 J) Determine the momentum lost in the collision (0.0 kgm/s)

Explanation / Answer

First momentum is always conserved whether it is an elastic orinelastic collision so there will be no momentum lost in thecollision. Knowning this, you can calculate the initial andfinal energies, because there is Kinetic energy loss in aninelastic collision. First you need to find the speed at the cart at the bottom ofthe ramp to see what the initial speed is before thecollision. To do this, you can assume all potential energy initial isconverted to kinetic energy final. mgh = 1/2mv2 v = 2gh = 2 * 9.8m/s2 *.15m =1.71m/s m1v1 +m2v2 =(m1 + m2)vf .5m/s * 1.71m/s = (.5 + 1.2)vf = 0.503m/s .5m/s * 1.71m/s = (.5 + 1.2)vf = 0.503m/s Initial KE = 1/2mv2 = 1/2 *.5 *(1.71m/s)2 = 0.735J Final KE = 1/2mv2 = 1/2 * 1.7 *(0.503m/s)2 = 0.215 KE = 0.735-0.215 = 0.52J Hope that helps

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