pendulum problem?

Question

a 15kg ball of radius 4cm is suspended from a point 2.94m above the floor by an iron wire of unstretched length 2.85m. the diameter of a wire is 0.090cm and it's young's modulus is 1.8*10to the 11 power N/msquared. if the ball is set swinging so that its center passes through the lowest point at 5m/s by how much does the bottom of the ball clear the floor?

Answer 1

That's a cute problem.

Young's Modulus E is related to the tension in the wire T, cross-sectional area A and change in length ΔL relative to original length L by the expression

T = E A ΔL / L

What we need now is the tension in the wire when the pendulum is at the lowest point. Centripetal force is

F = m v² / r

The wire must both support the weight of the mass AND provide that centripetal force, so the tension in the wire is

T = m v² / r + m g

Put it all together:

m v² / r + m g = E A ΔL / L

You know everything except the change in length ΔL (or you will when you cut the diameter in half to get radius, convert to meters, and compute A = π r²). Compute that, then you know how high the ball is from the floor at the lowest point of the swing.

Answer 2

At least enough to not hit the floor-otherwise WHY would build such a contraption?