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A small block slides down a frictionless track whose shape is described by yx/d

ID: 1517472 • Letter: A

Question

A small block slides down a frictionless track whose shape is described by yx/d for x0. The value of d is 14 meters, and x and y are measured in meters as usual. (a) Suppose the block starts from rest on the track, at - 1.5 meters. What will the block's speed be when m/s (b) Suppose the block starts on the track at x 0, and is given an initial velocity of 62 m/s to the left. The block then begins to slide up the track to the left. At what value of x will the block turn around and begin to slide down again? Answer: - m (c) Now suppose the blocks starts on the track at x = 1.6 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial velocity in this case? Answer: m/s (d) Suppose the block starts on the track at x = 0, what minimum initial velocity (moving to the right) must the block have such that it will leave the track at0 and go into freefall? Answer: m/s (e) You start the block on the track at rest, somewhere to the left of x = 0, You then release the block from rest and let it slide down. What is the maximum value of x from which you can release the block from rest and have it leave the track at x = 0 and go into freefall? (Note: your answer should be a negative number, since you're starting to the left of the origin.) Answer: m

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