Question

A uniform beam resting on two pivots has a length L=6.00 m and mass M=90.0 kg. The pivot under the left end exerts a normal force n₁ on the beam, and the second pivot located at a distance l=4.00 m from the left end exerts a normal force n₂. A woman of mass m=55.0 kg steps onto the left end of the beam and begins walking to the right as in the figure. The goal is to find the woman’s position when the beam begins to tip.

(a) What is the appropriate analysis model for the beam before it begins to tip?

(b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin.

(c) Where is the woman when the normal force n₁ is the greatest?

(d) What is n₁ when the beam is about to tip?

(e) Use the force equation of equilibrium to find the value of n₂ when the beam is about to tip.

(f) Using the result of part (d) and the force equation of equilibrium, with torques computed around the second pivot, find the woman’s position x when the beam is about to tip.

(g) Check the answer to part (e) by computing around the first pivot point.