Force for uniform circular motion

In summary, the problem involves an ice skater moving in a uniform circular motion of radius 0.545 m while holding onto a rope tied to a pole. The force exerted by the rope on her arms is 1.42674 kN, and the ratio of this tension to her weight is 2.3572. This can be calculated using the equation F=(mv^2)/r and the fact that the acceleration of gravity is 9.8 m/s^2.
  • #1
jj8890
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[SOLVED] Force for uniform circular motion

Homework Statement


A 61.7 kg ice skater is moving at 3.55 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.545 m around the pole. The acceleration of gravity is 9.8 m/s^2.
a. Find the force exerted by the rope on her arms. Answer in units of kN.
b. Find the ratio of this tension to her weight.

Homework Equations


F=(mv^2)/r


The Attempt at a Solution


I got a using the above equation:
F=((61.7) * (3.55)^2)/.545
F=1426.74 N or 1.42674 kN
I know this is right for part a, I just don't understand what they are asking for part b or what equation to use. I would appreciate any help.
 
Last edited:
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  • #2
Please help...I just need to figure out how I would start this. I understand now that the "tension" is the force that I calculated in (a) but I am unsure how to find the ratio of this tension to her weight (61.7 kg) i was thinking just diving 61.7/1.42674 but that does not seem right. I would greatly appreciate any help.
 
  • #3
Got it...thanks anyway...--->1426.74/(61.7 * 9.81)=2.3572
 
  • #4
Ratio is f/mg
 
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1. What is the definition of force for uniform circular motion?

The force for uniform circular motion is the centripetal force, which is the force that acts towards the center of the circular path and keeps an object moving in a circular motion at a constant speed.

2. How is the magnitude of the force for uniform circular motion determined?

The magnitude of the force for uniform circular motion is determined by the mass of the object, the speed of the object, and the radius of the circular path it is moving along. It can be calculated using the formula F = mv^2/r, where F is the force, m is the mass, v is the speed, and r is the radius.

3. What happens if the force for uniform circular motion is increased?

If the force for uniform circular motion is increased, the object will move in a larger circular path at a higher speed. The magnitude of the force is directly proportional to the speed and radius of the circular path, so an increase in force will result in an increase in speed or radius, or both.

4. Can an object in uniform circular motion have a constant velocity?

No, an object in uniform circular motion cannot have a constant velocity because its direction of motion is constantly changing. Velocity is a vector quantity that includes both speed and direction, so if the direction of motion is changing, the velocity is also changing.

5. What is the relationship between the force for uniform circular motion and the period of the motion?

The period of the motion, which is the time it takes for the object to complete one full revolution, is inversely proportional to the force for uniform circular motion. This means that as the force increases, the period decreases, and vice versa. This relationship can be seen in the formula T = 2πr/v, where T is the period, r is the radius, and v is the speed.

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