A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot is at a distance { from the left end. A woman of mass m starts at the left end and walks toward the right end as in the figure below. (a) When the beam is on the verge of tipping, find symbolic expression for the normal force exerted by the second pivot in terms of M, m, and g. n2 = (m+ m)g (b) When the beam is on the verge of tipping, find symbolic expression for the woman's position in terms of M, m, L, and {. (m + m)1 X = m (c) Find the minimum value of { that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.) min =

A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot is at a distance { from the left end. A woman of mass m starts at the left end and walks toward the right end as in the figure below. (a) When the beam is on the verge of tipping, find symbolic expression for the normal force exerted by the second pivot in terms of M, m, and g. n2 = (m+ m)g (b) When the beam is on the verge of tipping, find symbolic expression for the woman's position in terms of M, m, L, and {. (m + m)1 X = m (c) Find the minimum value of { that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.) min =

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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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot
is at a distance { from the left end. A woman of mass m starts at the left end and walks toward the right end as in the figure
below.
(a) When the beam is on the verge of tipping, find symbolic expression for the normal force exerted by the second
pivot in terms of M, m, and g.
n2 =
(m +m)g
(b) When the beam is on the verge of tipping, find symbolic expression for the woman's position in terms of M, m, L,
and l.
m
(m +m)1
2
X =
m
(c) Find the minimum value of { that will allow the woman to reach the end of the beam without it tipping. (Use any
variable or symbol stated above as necessary.)
min =
Negd

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