Anonymous

Question description

A beam resting on two pivots has a length of
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 placed a distance
ℓ = 4.00 m
from the left end exerts a normal force
n2.
A woman of mass
m = 54.0 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.
(b) Where is the woman when the normal force
n1
is the greatest?
x = m

(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.
x = m

(f) Check the answer to part (e) by computing torques around the first pivot point.
x = m

part 2
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 ℓ 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 a symbolic expression for the normal force exerted by the second pivot in terms of M, m, and g. (Enter the magnitude.)
n2 =

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

(c) Find the minimum value of ℓ that will allow the woman to reach the end of the beam without it tipping. (Use the following as necessary: m, M, and L.)
ℓmin =

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