Question

A beam resting on two pivots has a length of L = 6.00 m and mass M = 85.3 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivotplaced a distance l = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 54.8 kg steps onto the left end of the beam and begins walking to theright as in the figure below. The goal is to find the woman's position when the beam begins to tip.

(a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the first pivot, whichis the origin. (Do this on paper. Your instructor may ask you to turn in this work.)

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


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

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

(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 isabout to tip. Give her position as measured from the left end of the beam.
m

(f) Check the answer to part (e) by computing torques around the first pivot point. Give her position as measured from the left end of the beam.
m
(g) Except for possible slight differences due to rounding, is the answer the same?

Answer 1

a similar question is solved below, but with different values. hope this helps you.


A beam resting on two pivots has a length of L = 6.00 m and mass M = 73.8 kg. The pivot under the left end exerts a normal force n1 on the beam, and thesecond pivot placed a distance l = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 63.3 kg steps onto the left end of the beam andbegins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip.

(a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the firstpivot, which is the origin. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Where is the woman when the normal force n1 is the greatest?
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 n2 when the beam is about to tip.
3 N

(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 whenthe beam is about to tip.
4 m

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

(g) Except for possible slight differences due to rounding, is the answer the same?


b) the greatest N1 occurs when the woman is at the left end
c) N1 = 0 at the tipping point of the beam
d) N2 = (m + M) g N2 must support both woman and beam
where m = mass of woman and M = mass of beam
N2 = (73.8 + 63.3) * 9.8 = 1344 N
e) m g (x - 4) = M g * 1 balancing torque about N2
x = (M + 4 m) / m = (73.8 + 4 * 63.3) / 63.3 = 5.166 m from left end
Now taking torques about N1
3 M g + m g x = N2 * 4 = 1344 * 4 = 5374 N-m
x = (5374 - 3 * 73.8 * 9.8) / (63.3 * 9.8) = 5.165 m