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 15 m, and you use your watch to find that each loop around takes 25 s. you remember weighing yourself earlier in the day to be 780 n. what are your speed and the magnitude of your acceleration? what is your weight at the top of the ride? what is your weight at the bottom of the ride?

Answer 1

1. Speed: 2.26 m/s, Acceleration: 0.18 m/s²

2. Weight at the top: 822 N

3. Weight at the bottom: 738 N

Step-by-step explanation:

In the first step, we determined the speed and acceleration of the Ferris wheel ride. The speed was calculated using the formula v = 2πr/T, where v represents speed, π is a mathematical constant, r is the radius (15 meters), and T is the time for one loop around the wheel (25 seconds). Plugging in these values, we found the speed to be 2.26 m/s. The acceleration was then determined using the formula a = v²/r, resulting in an acceleration of 0.18 m/s².

Moving on to the second step, we considered your weight at the top of the ride. At this point, both gravitational force and centrifugal force contribute to your apparent weight. Using the formula W = mg + m * (v²/r), where W is weight, m is mass, g is the acceleration due to gravity, v is speed, and r is radius, we calculated the weight at the top to be 822 N.

In the third step, we explored your weight at the bottom of the ride. Here, only the gravitational force is in play, leading to a weight of W = mg, resulting in 738 N. These calculations showcase the interplay of gravitational and centrifugal forces in circular motion scenarios, offering insights into the physics behind amusement park rides.