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. Calculate the mass of the skaters.
m = 45.6 kg
To calculate the mass of the skaters, we can use the formula for the frequency of a simple harmonic oscillator:
f = 1 / (2π) * sqrt(k / m)
Where:
f is the frequency of revolution,
k is the spring constant,
m is the mass of the skaters.
Given that the frequency of revolution is 0.85 Hz and the spring constant is 650 N/m, we can rearrange the formula to solve for m:
m = k / (4π² * f²)
Plugging in the values for k and f:
m = 650 N/m / (4π² * (0.85 Hz)²)
Now we can compute the value of m using a calculator or computer program:
m = 650 N/m / (4 * 3.14159² * (0.85 Hz)²)
= 650 N/m / (4 * 9.8696 * 0.7225 Hz²)
≈ 650 N/m / (4 * 56.548 * 0.7225 Hz²)
≈ 650 N/m / (4 * 40.3132 Hz²)
≈ 650 N/m / (161.2528 Hz²)
≈ 650 N/m / 161.2528 Hz²
≈ 4.03 N/(m * Hz²)
Therefore, the mass of the skaters is approximately 4.03 kg.