Two frictionless tracks, A and B, span the same horizontal distance, however tra

Question

Two frictionless tracks, A and B, span the same horizontal distance, however track B has a dip of vertical depth h, as shown in the figure. The tracks are equipped with identical springs of spring constant k for launching identical balls of mass m. Before the launch, the balls are just touching the springs, which are compressed by an amount X. The balls are free of the springs when they have crossed the x = 0 position. We want to determine which ball crosses the x = d position first. (a) Which of the balls do you expect to be faster at position x = d/2? [1] the ball on track A [2] the ball on track B [3] both have the same speed. (b) Which of the balls do you expect to be faster at position x = d? [1] the ball on track A [2] the ball on track B [3] both have the same speed. (c) Which principle allows you to determine the speed of the balls at d/2 and d? (d) For each track, derive expressions for the speed of the ball at position x = d/2 and position x = d. Please make sure your answers agree with (a) and (b). (e) Which ball crosses the x = d position first? Part d of this question. When the ball is at d/2 on track B, I am unsure where exactly my (mgh) will go in the conservation of energy formula and how do i account for spring constant.

Explanation / Answer

You will have to take account of spring potential energy which is equal to 0.5*k*X^2. For more clarification you will have to upload the figure.

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