A beam resting on two pivots has a length of L= 6.00 m and mass M= 78.7 kg. The pivot under the left end exerts a normal force n2. A woman of mass m = 58.2 kg steps onto the left end of the beam and begins walking to the right. What is the womans position when the beam is about to tip?

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Ch 8 Problem 12: "A beam resting on two pivots has a length L=6m and mass M=78.3 kg. The pivot under the left end exerts a normalforce n1 on the beam, and the second pivot placed a distance l=4 mfrom the left and exerts a normal force n2. A woman mass m=59.2 kgsteps onto the left end of the beam and begins walking to the rightas in the figure below. The goal is to find the woman's positionwhen the beam begins to tip."

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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 at a distance l=4.00 m from the left end exerts a normal force n₂. A woman of mass m=55.0 kg steps onto the left end of the beam and begins walking to the right as in the figure. 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.

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

(e) Use the force equation of equilibrium to find the value of n₂ when the beam is about to tip.

(f) Using the result of part (d) and the force equation of equilibrium, 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 around the first pivot point.

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A beam resting on two pivots has a length of L = 6.00 m and mass M= 92.0 kg. The pivot under the left end exerts a normal force n1 onthe beam, and the second pivot placed a distance script i = 4.00 mfrom the left end exerts a normal force n2. A woman of mass m =50.0 kg steps onto the left end of the beam and begins walking tothe right as in the figure below. The goal is to find the woman'sposition when the beam begins to tip.
(a) Sketch a free-body diagram, labeling the gravitational andnormal forces acting on the beam and placing the woman x meters tothe right of the first pivot, which is the origin. (Do this onpaper. Your instructor may ask you to turn in this work.)

(b) Where is the woman when the normal force n1 is thegreatest?
1

(c) What is n1 when the beam is about to tip?
2. N

(d) Use the force equation of equilibrium to find the value of n2when the beam is about to tip.
3. N

(e) Using the result of part (c) and the torque equilibriumequation, with torques computed around the second pivot point, findthe woman's position when the beam is about to tip.
4. m

(f) Check the answer to part (e) by computing torques around thefirst pivot point.
5. m

Except for possible slight differences due to rounding, is theanswer the same?
6. Yes/No

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A beam resting on two pivots has a length of L= 6.00 m and mass M= 78.7 kg. The pivot under the left end exerts a normal force n2. A woman of mass m = 58.2 kg steps onto the left end of the beam and begins walking to the right. What is the womans position when the beam is about to tip?

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