A uniform beam resting on two pivots has a length 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 secondpivot located a distance ℓ = 4.00 m from the left end exerts a normal force nℓ. A womanof mass m = 55.0 kg steps onto the left end of the beam and begins walking to the rightas in Figure P12.24. The goal is to find the woman’s position when the beam begins totip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b)Sketch a force diagram for the beam, labeling the gravitational and normal forcesacting 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 n1is the greatest?(d) What is n1 when the beam is about to tip? (e) Use Equation 12.1 to find the value ofn2 when the beam is about to tip. (f) Using the result of part (d) and Equation 12.2,with torques computed around the second pivot, find the woman’s position x when thebeam is about to tip. (g) Check the answer to part (e) by computing torques around thefirst pivot point.Figure P12.24
A uniform beam resting on two pivots has a length 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 located a distance ℓ = 4.00 m from the left end exerts a normal force nℓ
. 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 P12.24. 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? (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?
(d) What is n1 when the beam is about to tip? (e) Use Equation 12.1 to find the value of
n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 12.2,
with torques computed around the second pivot, find the woman’s position x when the
beam is about to tip. (g) Check the answer to part (e) by computing torques around the
first pivot point.
Figure P12.24
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