<p>A beam resting on two pivots has a length of L = 6.00 m and mass M = 104.1 kg

Question

<p>A beam resting on two pivots has a length of L = 6.00 m and mass M = 104.1 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 = 57.9 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. <br /><br />(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, which is the origin.<br /><br />(b) Where is the woman when the normal force n1 is the greatest? <br /> <br /><br />(c) What is n1 when the beam is about to tip? <br /> <br /><br />(d) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip. <br /> <br /><br />(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.<br /><br /><br />(f) Check the answer to part (e) by computing torques around the first pivot point. <br /><br />(g) Except for possible slight differences due to rounding, is the answer the same?</p>

Explanation / Answer

a) the greatest N1 occurs when the woman is at the left end b) N1 = 0 at the tipping point of the beam c) n1 is equal to 0 at this point because it is no longer in contact with the pivot point. d) Like the problem says, use the force equilibrium equation. Wwoman = (9.8x50) Wbeam = (9.8x92) F = n1 + n2 - Wwoman - Wbeam = 0 Since n1 is equal to 0, the equation becomes: n2 = Wwoman + Wbeam. n2 = 9.8(92 + 50) n2 = 1391.6 N e) Remember that torque is the force times the length of the position vector. L/2 = 3 4(n2) = (Wwoman)X + (Wbeam)(3) Plug in the values and solve for X 1391.6*4 = (50*9.8)X + (92*9.8)(3) X = 5.84 f) This answer is the exact same as the answer for e.

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