Chapter 8, Problem 22P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A beam resting on two pivots has a length of 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 placed 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 Figure P8.22. The goal is to find the woman’s position when the beam begins to tip. (a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the first pivot, which is the origin, (b) Where is the woman when the normal force n1 is the greatest? (c) What is n1 when the beam is about to tip? (d) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip. (e) Using the result of part (c) and the torque equilibrium equation, with torques computed around the second pivot point, find the woman’s position when the beam is about to tip. (f) Cheek the answer to part (e) by computing torques around the first pivot point. Except for possible slight differences due to rounding, is the answer the same?Figure P8.22

(a)

To determine
The free body diagram for the beam resting on two pivots.

Explanation

The following figure shows the free body diagram of Normal force and gravitational force acting on the beam is,

(b)

To determine
The position of the woman when the normal force n1 is the greatest.

(c)

To determine
The normal force n1 when the beam is about to tip

(d)

To determine
The normal force n2 when the beam is about to tip.

(e)

To determine
The woman’s position when the beam is about to tip.

(f)

To determine
The woman’s position when the beam is about to tip.

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