F = m * (0.85 Hz)^2 * 2πm = F / (0.85 Hz)^2 * 2π Calculate Mass of Skaters

[hinamori88]

Homework Statement

Two identical ice skaters are holding onto opposite ends of a very long spring with a spring constant of 650 N/m. While spinning in a circle, the skaters frequency of revolution is measured to be 0.85 Hz. What is the mass of the skaters?

Homework Equations

F = kx

The Attempt at a Solution

F = (650 N/m)x ?

 

[ehild]

Remember, circular motion is the resultant of two perpendicular SHM with the same frequency and amplitude and phase difference of pi/2. ehild

 

[hinamori88]

Oh so then u use the equation
f=(1/2∏)√(k/m)
And the m needs to be 2m...ok got it!

Thank you!

 

[ehild]

No, m is not twice that of one skater-just the opposite.

Both skaters spin along the same circle. The situation is the same for each of them as if there was a pole at the centre, and half of the spring connected to the pole with one end and the other end to the skater. What is the spring constant of a halved spring?

ehild

 

[asteriatic]

The equation F = kx is for calculating the force exerted by a spring, where k is the spring constant and x is the displacement from equilibrium. This equation does not apply to the given scenario, where we are trying to calculate the mass of the skaters.

To calculate the mass of the skaters, we can use the formula F = ma, where F is the centripetal force, m is the mass, and a is the centripetal acceleration. We can rearrange this equation to solve for m:

m = F / a

The centripetal force in this scenario is provided by the tension in the spring, which can be calculated using the formula for centripetal force:

F = m * (0.85 Hz)^2 * 2π

Substituting this into the equation for mass, we get:

m = [m * (0.85 Hz)^2 * 2π] / a

The centripetal acceleration can be calculated using the formula a = v^2 / r, where v is the linear velocity and r is the radius of the circle. In this case, the skaters are holding onto opposite ends of the spring, so the radius of the circle is equal to the length of the spring. The linear velocity can be calculated using the formula v = 2πr * f, where f is the frequency of revolution. Substituting these values into the equation for acceleration, we get:

a = [2πr * f]^2 / r

Simplifying this, we get:

a = (4π^2 * r * f^2) / r

The radius of the circle is equal to the length of the spring, which is not given in the problem statement. So, we cannot calculate the exact value of the mass of the skaters without knowing the length of the spring. However, we can still provide a general formula for the mass of the skaters:

m = [m * (0.85 Hz)^2 * 2π] / [(4π^2 * r * f^2) / r]

This can be simplified to:

m = [m * (0.85 Hz)^2 * r] / (4π^2 * f^2)

In conclusion, the mass of the skaters can be calculated using the formula m = [m * (0.85 Hz)^2 * r] / (4π^2 *