Circular and Satellite Motion Legacy Problem #4 Guided Solution
Problem*
Elmira, New York boasts of having the fastest carousel ride in the world. The merry-go-round at Eldridge Park takes riders on a spin at 18 mi/hr (8.0 m/s). The radius of the circle about which the outside riders move is approximately 7.4 m.
- Determine the time for outside riders to make one complete circle.
- Determine the acceleration of the riders.
Audio Guided Solution
A good problem solver reads the problem very carefully and begins to identify the known quantities and the unknown quantities, and then uses physics concepts to get from the known information to the unknown information. Here we have a problem about riders on a merry-go-round. We're told that they travel at a speed of 8.0 meters per second. We're told they're moving in a circle that is 7.4 meters in radius. We're asked two things about these riders. First of all, we're asked the time it takes to make one complete circle, and second, we're asked to determine their acceleration. We'll start with point A, in which we have to calculate the time. Now what we know about objects moving in circles is we know that the speed is the distance per time, and that the time is often expressed as the time for one circle, and when it's done that way, the distance traveled is the circumference of one circle. So here what we can do is take the equation v equal d over t and rearrange it to solve for t. And we can say that the t, the t for one complete circle, is equal to the d divided by the v, where the d is the distance for one complete circle. That distance for one complete circle is the circumference, it's 2 pi times the radius of 7.4 meters. We have to divide it by 8.0 meters per second, and doing so gets us the time for one circle to be 5.8 seconds. Now in part B, we wish to calculate the acceleration. For objects moving in circles, there's a special case of the acceleration being the speed squared divided by the radius. Here our riders are moving at 8.0 meters per second, and the radius of the circle is 7.4 meters. So we take 8.0 and we square it, we divide by 7.4, and we get 8.65 meters per second per second. We can round that to two digits as 8.7 meters per second per second.
Solution
- 5.8 s
- 8.7 m/s/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{m}{m,mass} = 61.7\unit{kg}\), \(\descriptive{v}{v,velocity} = 18.5 \unit{\meter\per\second}\), \(\descriptive{R}{R,radius} = 30.9\unit{m}\), \(F_\text{norm} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Circular and Satellite Motion at The Physics Classroom Tutorial.