Question

Two steel pipes (with Young's modulus E=200*10^9 N/m^2) are anchored within a concrete wall so they stick out horizontally, parallel to the ground below. They each have a length of l=2.0 m, but the lower one is solid with a radius r=2.0 cm and the upper one is hollow with an inner radius b=2.0 cm. A person with a mass of 70 kg then alternately stands on the free end of either pipe, causing each pipe to bend the same amount. Note, the are moment of intertia of a solid cylinder is 1/4(pi)r^4, and that for a hollow cylinder is 1/4(pi)(a^4-b^4) where a is the outer radius and b is the inner radius of the hollow pipe.

What is the outer radius a of the hollow pipe?

What is the magnitude of the torque due to the weight of the person (standing on the free end of apipe) about a rotational axis located where the pipe is anchored to the wall?

What is the radius of curvature of either bent pipe when the person stands on its end? You may neglect the pipe's weight.

Answer 1