### Physics Problem: Beam and PivotA beam of length \( L \) and mass \( M \) rests on two pivots. The first pivot is at the left end, considered the origin, and the second pivot is at a distance \( \ell \) from the left end. A woman of mass \( m \) starts at the left end and walks toward the right end as shown in the figure below.#### Diagram ExplanationThe diagram shows a horizontal beam resting on two upward-pointing arrows representing the pivots. The beam has length \( L \), with its left end at the origin. The second pivot is located at distance \( \ell \) from the left end. A woman is walking on the beam, and her distance from the left end is marked as \( x \).#### Problems**(a)** When the beam is on the verge of tipping, find a symbolic expression for the normal force \( n_2 \) exerted by the second pivot in terms of \( M \), \( m \), and \( g \).\[ n_2 = \underline{\hspace{3cm}} \]**(b)** When the beam is on the verge of tipping, find a symbolic expression for the woman's position \( x \) in terms of \( M \), \( m \), \( L \), and \( \ell \).\[ x = \underline{\hspace{3cm}} \]**(c)** Find the minimum value of \( \ell \) that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.)\[ \ell_{\text{min}} = \underline{\hspace{3cm}} \]

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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 e 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 = (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 f. (c) Find the minimum value of e 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 e 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 = (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 f. (c) Find the minimum value of e 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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### Physics Problem: Beam and Pivot

A beam of length \( L \) and mass \( M \) rests on two pivots. The first pivot is at the left end, considered the origin, and the second pivot is at a distance \( \ell \) from the left end. A woman of mass \( m \) starts at the left end and walks toward the right end as shown in the figure below.

#### Diagram Explanation
The diagram shows a horizontal beam resting on two upward-pointing arrows representing the pivots. The beam has length \( L \), with its left end at the origin. The second pivot is located at distance \( \ell \) from the left end. A woman is walking on the beam, and her distance from the left end is marked as \( x \).

#### Problems

**(a)** When the beam is on the verge of tipping, find a symbolic expression for the normal force \( n_2 \) exerted by the second pivot in terms of \( M \), \( m \), and \( g \).

\[ n_2 = \underline{\hspace{3cm}} \]

**(b)** When the beam is on the verge of tipping, find a symbolic expression for the woman's position \( x \) in terms of \( M \), \( m \), \( L \), and \( \ell \).

\[ x = \underline{\hspace{3cm}} \]

**(c)** Find the minimum value of \( \ell \) that will allow the woman to reach the end of the beam without it tipping. (Use any variable or symbol stated above as necessary.)

\[ \ell_{\text{min}} = \underline{\hspace{3cm}} \]

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