In a skating stunt known as "crack-the-whip", a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 76.7 kg and is 6.18 m from the pivot. He is skating at a speed of 6.72 m/s. Determine the magnitude of the centripetal force that acts on him.
To determine the magnitude of the centripetal force acting on the skater, you need to use the centripetal force formula:
F = (m * v^2) / r
where:
F is the centripetal force,
m is the mass of the skater,
v is the velocity of the skater,
and r is the radius (distance from the pivot to the skater).
We are given the following values:
m = 76.7 kg
v = 6.72 m/s
r = 6.18 m
Plug these values into the formula to calculate the centripetal force:
F = (76.7 kg * (6.72 m/s)^2) / 6.18 m
Now, calculate the value:
F = (76.7 kg * 45.0624 m^2/s^2) / 6.18 m
F = 3427.8048 kg·m/s^2 / 6.18 m
F ≈ 554.95 N
Therefore, the magnitude of the centripetal force acting on the skater is approximately 554.95 Newtons.