a 82.7 kg ice skater is moving at 5.88 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 0.627 m around the pole. the acceleration of gravity is 9.8 m/s^2. Find the force exerted by the rope on her arm.
The centripetal force, which is applied by the rope, would be M V^2/R, where R is the length of the rope. The value of g does not affect that force, but it does affect her weight on the ice.
ywa
To find the force exerted by the rope on the ice skater's arm, we need to use the principles of centripetal force.
1. First, we need to calculate the centripetal acceleration of the ice skater moving in a circle. The centripetal acceleration (a) can be calculated using the formula:
a = (v^2) / r
where:
- v is the tangential velocity of the ice skater (5.88 m/s in this case)
- r is the radius of the circle (0.627 m in this case)
Plugging in the given values, we have:
a = (5.88 m/s)^2 / 0.627 m = 55.3 m/s^2
2. The centripetal acceleration (a) is related to the net force (F) acting on the ice skater by the equation:
F = m * a
where:
- m is the mass of the ice skater (82.7 kg in this case)
- a is the centripetal acceleration (55.3 m/s^2 in this case)
Plugging in the given values, we have:
F = (82.7 kg) * (55.3 m/s^2) = 4560.71 N
Therefore, the force exerted by the rope on the ice skater's arm is approximately 4560.71 Newtons (N).
Note: The mass of the skater is given, and we assume that the acceleration is solely due to the circular motion. We disregard the force of gravity on the skater in this calculation.