Answered: A uniform beam resting on two pivots…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A uniform beam resting on two pivots has a length L = 6.00 m and mass M = 87.0 kg. The pivot under the left end exerts a normal force n₁ on the beam, and the second pivot located a distance ℓ = 4.00 m from the left end exerts a normal force n₂. A woman of mass m = 52.5 kg steps onto the left end of the beam and begins walking to the right as in the figure below. 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?

rigid object in static equilibrium

particle in equilibrium

rigid object under net force

particle under net force

(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?
x = m

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

(e) Use Σ _ext = 0 to find the value of n₂ when the beam is about to tip.
N

(f) Using the result of part (d) and Σ _ext = 0, with torques computed around the second pivot, find the woman's position x when the beam is about to tip.
m

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

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