Circular and Satellite Motion Legacy Problem #7 Guided Solution
Problem*
Dominic is the star discus thrower on South's varsity track and field team. In last year's regional competition, Dominic whirled the 1.6 kg discus in a circle with a radius of 1.1 m, ultimately reaching a speed of 52 m/s before launch. Determine the net force acting upon the discus in the moments before launch.
Audio Guided Solution
A good problem solver reads the problem carefully, developing a mental picture of what's going on, identifies the known quantities and the unknown quantities, and then develops a strategy to get from the known information to the unknown information. Here we have a picture in our mind of a discus that's moving in a circle. The discus thrower is spinning in a circle, holding the discus at arm's length, and the discus spins in a circle with a radius of 1.1 meters. It has a mass of 1.6 kilograms, and it eventually accumulates a speed of 52 meters per second. What we're asked to determine is the net force acting upon the discus at the moment before launch, that is, when it finally has acquired this 52 meters per second speed. To do this, we have to relate the net force to the mass and the acceleration, and the acceleration to the speed and the radius. I notice that we're given the speed of 52 meters per second and the radius of 1.1. For the objects moving in circles, the acceleration would be calculated as the speed squared over the radius. So we're going to take the 52 and square it and divide by 1.1 meters. The number on your calculator becomes the acceleration, and to get the net force, we would take this acceleration and multiply it by the mass of 1.6 kilograms. Doing that gives us 3,933.09 newtons. Rounding to two significant digits, it would be 3.9 times 10 to the third newtons.
Solution
3.9 x 103 N
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.