Problem: An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 5.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s.Given the angular speed of ω = 5.00 radians/s, find the radius R(ω) at which the mass rotates without moving toward or away from the origin.

FREE Expert Solution

Hooke's law:

F = K·x

Centripetal force:

Fc=mv2r=mrω2

The force on the spring is equal to the centripetal force.

k•Δx = mrω2 

View Complete Written Solution
Problem Details

An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 5.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s.

Given the angular speed of ω = 5.00 radians/s, find the radius R(ω) at which the mass rotates without moving toward or away from the origin.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Uniform Circular Motion concept. You can view video lessons to learn Uniform Circular Motion. Or if you need more Uniform Circular Motion practice, you can also practice Uniform Circular Motion practice problems.