Circular and Satellite Motion Legacy Problem #6 Guided Solution
Problem*
In the display window of the toy store at the local mall, a battery-powered plane is suspended from a string and flying in a horizontal circle. The 631-gram plane makes a complete circle every 2.15 seconds. The radius of the circle is 0.950 m. Determine the velocity of, acceleration of, and net force acting upon the plane.
Audio Guided Solution
A good problem solver reads the problem carefully and begins to identify the known and the unknown quantities, and then begins to use physics equations and conceptual reasoning to think about a strategy to get from the known information to the unknown information. Here we have a problem about a plane, a toy plane, that is flying within a circle. The mass of the plane is 631 grams. Not a great unit for expressing mass, so we're going to convert it right away to 0.631 kilograms. We're told that the plane is traveling in a circle, and it takes 2.15 seconds to make a complete circle. And we're told the radius of the circle through which it moves is 0.950 meters. We're to calculate three physics quantities, one being the velocity of the plane, the other being the acceleration, and the third being the net force. We'll begin with velocity, which can be calculated as the distance traveled per time of travel. For this plane, the distance traveled could be taken as a single circumference, and the time of travel could be taken as a time for that circumference. That's a time of 2.15 seconds in the denominator. In the numerator, the circumference is 2 pi times 0.95 meters. When you do your math, you get 2.7763 meters per second, and we can express this to three digits as 2.78 meters per second. Now to get the acceleration for objects moving in circles, we have the special case of the acceleration being speed squared over the radius. The radius in the denominator is 0.950 meters, and in the numerator, we have to square our speed. So we take 2.7763 meters per second from point A, and we square it. We divide by 0.950 meters, and we get 8.1135 meters per second per second. Rounding to three digits, we can express it as 8.11 meters per second per second. Now finally, to get the net force, it's always, whether in a circle or not, it's always m times A. Here we have the m of 631 grams, or better yet, 0.631 kilograms. We have to take that mass and multiply it by the acceleration from part P, 8.1135 meters per second per second. When we do, we get 5.1196 newtons. We can round that to the third digit, it's 5.12 newtons.
Solution
velocity: 2.78 m/s
acceleration: 8.11 m/s/s
net force: 5.12 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.