Make sure you follow the Format outlined in the \"Standard for Homework Problem

Question

Make sure you follow the Format outlined in the "Standard for Homework Problem H for Solving the Problem. Draw your FREE BODY DIAGRAM, if appropriate, show yo WORK and Don't Forget to include the UNITS. A railroad freight car weighing 32 tons and traveling at 5.0 ft/s overtakes one weighing 24 tons and traveling at 3.0 ft/s in the same direction. If the cars couple together, find (a) the speed of the cars after collision and (b) the loss of kinetic energy during collision. (c) If instead, as is very unlikely, the collision is elastic, find the speeds of the cars after collision.

Explanation / Answer

(A) Applying momentum conservation,

(32 x 5) + (24 x 3) = (32+ 24) v

v = 4.14 ft/s .......Ans

(b) KEi = (32000)(5x0.3048 m/s)^2 / 2 + (24000)(3 x 0.3048)^2 / 2

KEi = 47194.74 J

KEf = (32000 + 24000) (4.14 x 0.3048)^2 / 2

= 44585 J

Energy loss = Kei - KEf

= 2609.74 J

(c) if collision is elastic then,

velociy of approach = velocity of separation

5 - 3 = v2 - v1

v2 = 2 + v1

Applying momentum conservation,

(32 x 5) + (24 x3) = 32v1 + 24v2

232 = 32v1 + (24)(2 + v1)

v1 = 3.29 ft/s .....velocity of 32 tons.

v2 = 5.29 ft/s ....velocity of 24 tons car.

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