Circular and Satellite Motion Legacy Problem #8 Guided Solution
Problem*
Landon and Jocelyn are partners in pair figure skating. Last weekend, they perfected the death spiral element for inclusion in their upcoming competition. During this maneuver, Landon holds Jocelyn by the hand and swings her in a circle while she maintains her blades on the ice, stretched out in a nearly horizontal orientation. Determine the net force which must be applied to Jocelyn (m=51 kg) if her center of mass rotates in a circle with a radius of 61 cm once every 1.9 seconds.
Audio Guided Solution
A good problem solver reads the problem carefully and identifies the known quantity and the unknown quantity and then uses physics understanding and reasoning to think out a strategy to get from the known information to the unknown information. Here in this problem we have Landon who is spinning Jocelyn in a circle. We're told that Jocelyn's center is 61 centimeters from the center of the circle and she makes one complete circle every 1.9 seconds. Her mass is 51 kilograms. What we're asked to determine is the net force acting up on Jocelyn. So as I think about my relationships, I think about net force being m times a and then I think about for circles, a being the special case of v squared over r. And then when I think of v, I'm thinking of that's got to be a circumference divided by a period or at least some sort of distance divided by a corresponding time. And here what I have is the time for a circle and the radius of a circle, sufficient information for me to calculate the speed. And once I get the speed, the speed along with the radius is sufficient information to calculate the acceleration. Once I get that to that point, it's business as usual for me because I know f net is always equal to m times that a. So the way I'll approach this is I'll begin by calculating the speed of Jocelyn as she goes in the circle. I'll have to go the 2 pi r of 0.61 divided by 1.9 seconds. That gets me a speed of 2.0172 meters per second. Now if I square that speed and then divide by the radius of 0.61 meters, I'll have the acceleration. 2.0172 squared divided by 0.61 comes out to be 6.6709 meters per second per second. Now I need to take that acceleration and go f net equals ma, where the m is 51 kilograms. When I do that, I get 340.21 newtons. You can round that to two significant digits. The answer is 340 newtons.
Solution
340 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.