By pumping your legs back and forth, you manage to get swinging from an initial

Question

By pumping your legs back and forth, you manage to get swinging from an initial height of about 3 feet above the ground (when the swing is at rest) to a maximum height of 6 feet above the ground. You estimate that the swing seat has a mass of about 1 kg.

8.96 J transferred into the swing , 2.99m/s

You happen to remember someone telling you that for small enough angles, the function sin(x) is well approximated by the value of x. You realize that a frictionless swing acts a lot like a spring---the net force behaves like a restoring force. You estimate your swing's chain to have a length of about 17 feet. By thinking through the forces that yield a net force on you and the swing seat, and treating the angle that the swing's chain makes with the vertical as small, you try to develop a model of the net force from the swing as a simple restoring force. What would the associated restoring force constant be assuming your mass is about 75 kg?

Explanation / Answer

F = kx for spring

restoring force will be mgsin(theta) which can be approximated as mg(theta)

mg(theta) = kx

k = (mg(theta) )/x

this would be the amount of restoring force constant

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.