While at the county fair, you decide to ride the Ferris wheel. Having eaten too
ID: 2094917 • Letter: W
Question
While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 16m, and you use your watch to find that each loop around takes 25s. (a) What is your speed? (b) What is the magnitude of your acceleration? (c) What is the ratio of your weight at the top of the ride to your weight while standing on the ground? (d) What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground? While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 16m, and you use your watch to find that each loop around takes 25s. (a) What is your speed? (b) What is the magnitude of your acceleration? (c) What is the ratio of your weight at the top of the ride to your weight while standing on the ground? (d) What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground?Explanation / Answer
It always cracks me up when they write problems like this. My optics prof used to formulate questions like "you're at a gas station, filling up, and someone walks over and asks you a question about Malus' law". Anyway, here goes: You know the radius of the wheel, from there you can get the total distance around the wheel. Use that and the time taken to complete a loop to get the velocity. distance, d = 12*2*pi, time, t = 26s velocity, v = d / t Because this is a loop, we make use of angular acceleration to find how your weight changes at the top and the bottom. At all points along the wheel you are accelerating towards the center. Gravity, however, stays for all intents and purposes, constant. So first we say angular acceleration, a = v^2 / r, where v is the velocity found earlier, r is the radius of the wheel. Now as we established earlier, at the top you are accelerating downwards. Note that you are going to subtract this acceleration from gravity, not add to it. If you are confused by the sign convention, think of it this way: if you were falling fast enough, you would feel weightless. And the converse is true, if you were accelerating upwards, you feel heavier. So "true" weight = m*g, "apparent" weight = m*(g - a) for conditions at the top of the wheel. So Wapp/ W = m*(g-a) / m*g, the m's cancel At the bottom, true weight is the same, but apparent weight = m*(g + a) So Wapp/ W = m*(g+a) / m*g, the mass cancels again.
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