Centripetal force of an ice skater

AI Thread Summary
The problem involves a 55.5 kg ice skater moving at 4.02 m/s while holding onto a rope tied to a pole, creating circular motion with a radius of 0.807 m. The centripetal force exerted by the rope on her arms is calculated using the formula FC = mv²/R, resulting in a force of 1111.4 N. Additionally, there is a comparison of this force to her weight, but it is noted that the weight calculation requires using her mass multiplied by the acceleration due to gravity, not just her mass. The ratio of the force to her weight is incorrectly calculated as 20.02, highlighting the importance of using the correct weight value in such comparisons. Understanding the distinction between mass and weight is crucial in solving physics problems related to circular motion.
mandy9008
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Homework Statement


A 55.5 kg ice skater is moving at 4.02 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 0.807 m around the pole. (a) Determine the force exerted by the horizontal rope on her arms. (b) Compare this force with her weight by finding the ratio of the force to her weight.

Homework Equations


FC = mv2 / R


The Attempt at a Solution


a. FC = (55.5 kg)(4.02 m/s)2 / 0.807 m
FC = 1111.4 N

b. 1111.4 N / 55.5 kg = 20.02 ?
 
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mandy9008 said:

Homework Statement


A 55.5 kg ice skater is moving at 4.02 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 0.807 m around the pole. (a) Determine the force exerted by the horizontal rope on her arms. (b) Compare this force with her weight by finding the ratio of the force to her weight.

Homework Equations


FC = mv2 / R


The Attempt at a Solution


a. FC = (55.5 kg)(4.02 m/s)2 / 0.807 m
FC = 1111.4 N

b. 1111.4 N / 55.5 kg = 20.02 ?
her weight is not 55.5 kg. That's her mass.
 

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