Circular and Satellite Motion Legacy Problem #3 Guided Solution
Problem*
During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm.
- Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel.
- Determine the acceleration of the clothes.
Audio Guided Solution
A good problem solver reads the problem carefully, identifying the known quantities and the unknown quantities, and then uses physics concepts to plot out a strategy as to how to get from the known to the unknown. Here we have a problem about clothes in a washing machine. We're told that these clothes spin around in a circle that makes 1800 revolutions every minute. The radius of this barrel is 26 centimeters, but the clothes are plastered against the barrel. We're told to determine two quantities, the v, or speed of the clothes in meters per second, and the acceleration of the clothes. For the speed, we need to go distance to time. Distance to time ratio. The distance will be the distance for 1800 revolutions. That's 1800 circumferences. That's 1800 times 2 times pi times .26 meters. That gives us the distance traveled in a time of 60 seconds. If we do the division, we get for the numerator 2940.5 meters, and the denominator is 60 seconds. That comes out to be 49.0 meters per second. That's the speed of these clothes. For objects moving in a circle, the acceleration is simply the speed squared divided by the radius. So we need to take the result from our part A solution and square it, 49 squared, and then divide that by the radius, .26 meters. And that gives us 9238 meters per second per second, or 9.2 times 10 to the third meters per second per second.
Solution
- 49 m/s
- 9.2 x 103 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.