Inelastic collisions in one dimension: A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision, the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

Question

Quizplus · Accepted Answer

The kinetic energy before the collision can be calculated using the formula $KE = \frac{1}{2}mv^2$ for each object and then adding them together. For the 2.00-kg object, $KE_1 = \frac{1}{2}(2.00\,kg)(20.0\,m/s)^2 = 400\,J$. For the 3.00-kg object, $KE_2 = \frac{1}{2}(3.00\,kg)(10.0\,m/s)^2 = 150\,J$. The total initial kinetic energy is $400\,J + 150\,J = 550\,J$.After the collision, the 2.00-kg object moves west at 5.00 m/s, so its kinetic energy is $KE_1' = \frac{1}{2}(2.00\,kg)(5.00\,m/s)^2 = 25\,J$. The velocity of the 3.00-kg object after the collision isn't given, but we don't need it to find the kinetic energy lost. We know the total initial kinetic energy and the final kinetic energy of the 2.00-kg object. The 3.00-kg object's final kinetic energy isn't directly needed because the question asks for the total kinetic energy lost, not the final state of both objects.The kinetic energy lost is the initial total kinetic energy minus the final kinetic energy of the 2.00-kg object (since the question implies that the 3.00-kg object's final kinetic energy contributes to the total loss). Thus, the kinetic energy lost is $550\,J - 25\,J = 525\,J$.However, none of the provided options exactly match this calculation. Given the options, it seems there might have been a mistake in my calculation or interpretation of the options. Re-evaluating the options and the calculation process, the correct approach to find the kinetic energy lost involves calculating the total kinetic energy before and after the collision correctly, then subtracting the after from the before. If there was a mistake in the arithmetic or in the interpretation of the final state of both objects, that could explain the discrepancy. The correct answer should be based on the total kinetic energy before and after the collision, but without the exact final state of the 3.00-kg object, a precise calculation can't be completed as initially described. The correct answer choice should be selected based on the closest match to the expected loss in kinetic energy, considering the initial and given final conditions.

Inelastic Collisions in One Dimension: a 2