Circular and Satellite Motion Legacy Problem #1 Guided Solution
Problem*
During their physics field trip to the amusement park, Tyler and Maria took a rider on the Whirligig. The Whirligig ride consists of long swings which spin in a circle at relatively high speeds. As part of their lab, Tyler and Maria estimate that the riders travel through a circle with a radius of 6.5 m and make one turn every 5.8 seconds. Determine the speed of the riders on the Whirligig.
Audio Guided Solution
A good problem solver reads the problem carefully and develops a mental picture of what's going on, identifying the known quantities and the unknown quantity, and then uses physics principles to plot out a strategy as to how to get from the known to the unknown quantity. In this problem, we read of two students who are going on a circular ride at an amusement park. We're told that they're traveling in a circle, and the radius of the circle is 6.5 meters. We're told that they make one turn every 5.8 seconds. We're to determine the speed of the riders. The speed of any object is simply the distance to time ratio for that object, and when moving in a circle, we can consider one time around the circle as being the period, and the distance being equivalent to 2 pi r, or the circumference of that circle. So here, if we wish to determine the speed, we have to go 2 pi r divided by the period, or 2 pi times 6.5 meters divided by the time of 5.8 seconds. Doing that gives us 7.0415 meters per second. We can round to two digits, such that the answer is 7.0 meters per second.
Solution
7.0 m/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.