Circular and Satellite Motion Legacy Problem #2 Guided Solution
Problem*
The tallest Ferris wheel in the world is located in Singapore. Standing 42 stories high and holding as many as 780 passengers, the Ferris wheel has a diameter of 150 meters and takes approximately 30 minutes to make a full circle. Determine the speed of riders (in m/s and mi/hr) on the Singapore Flyer. (GIVEN: 1.00 m/s= 2.24 mi/hr)
Audio Guided Solution
A good problem solver reads the problem carefully, identifying the known information and the unknown quantity, and then uses physics concepts to plan out a strategy to get from the known to the unknown. Here we have a problem about riders on a Ferris wheel. They're making one complete circle in 30 minutes. The diameter of the circle through which they move is 150 meters. We wish to find the speed, so we need a distance-to-time ratio. For our time, we'll take 30 minutes, which is the same as 1,800 seconds. For our distance, we'll find the time for one complete circle, which is simply the circumference, or pi times d. Going pi times 150 meters gets us 471.24 meters. Dividing that by 1,800 seconds gives us the speed in meters per second. It comes out to be 0.26 meters per second. If we take the unrounded value, 0.2618 meters per second, and multiply by 2.24, we'll receive the speed in units of miles per hour, and it is 0.58 miles per hour.
Solution
0.26 m/s or 0.59 mi/hr
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.