A 64.0-kg ice skater is moving at 3.99 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 0.850 m around the pole. (a) Determine the magnitude of the force exerted by the horizontal rope on her arms. 1.13 kN (b) Compare this force with her weight. Frope W

Explanation:

The magnitude of the force exerted by the horizontal rope is expressed as

F = mv²/r

m is the mass of the ice skater = 64kg

v is the velocity = 3.99m/s

r is the radius of the pole = 0.850m

Substitute into the formula:

F = 64(3.99)²/0.850

F = 1,018.8864/0.850

F = 1,198.69N

Hence the magnitude of the force exerted by the horizontal rope on her arms is 1,198.69N or 1.199kN

b) Calculate the weight of the rope

Weight = mass * acceleration due to gravity

Weight = 64 * 9.81

Weight = 627.84N

Compare both by finding the ratio of the force to the weight

F/W = 1,198.69N/627.84

F/W = 1.91

F/W ≈ 2

F ≈ 2W

Hence the magnitude of the force is approximately twice that of the weight of the skater.