A woman of mass m = 53.8 kg sits on the left end of a seesaw—a plank of length L

Question

A woman of mass m = 53.8 kg sits on the left end of a seesaw—a plank of length L = 3.95 m, pivoted in the middle as shown in the figure. (a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M = 75.2 kg sit if the system (seesaw plus man and woman) is to be balanced? Changed: Your submitted answer was incorrect. Your current answer has not been submitted. Your response differs from the correct answer by more than 100%. m (b) Find the normal force exerted by the pivot if the plank has a mass of mpl = 11.3 kg. Correct: Your answer is correct. N (c) Repeat part (a), but this time compute the torques about an axis through the left end of the plank. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m EXERCISE HINTS: GETTING STARTED | I'M STUCK! Suppose a 31.3-kg child sits 0.91 m to the left of center on the same seesaw as the problem you just solved in the PRACTICE IT section. A second child sits at the end on the opposite side, and the system is balanced. (a) Find the mass of the second child. kg (b) Find the normal force acting at the pivot point. N

Explanation / Answer

Here ,

a) mass of woman , m = 53.8 Kg

L = 3.95 m

mass of man , M= 75.2 Kg

by balancing the moment of forces about the pivot

M * (x) * g - m * g * L/2 = 0

75.2 * x - 53.8 * 3.95/2 = 0

x = 1.413 m

the man should be 1.413 m from the pivot.

b)

Normal force at the pivot

N = m * g + M * g + mp * g

N = (53.8 + 75.2 + 11.3) * 9.8

N = 1375 N

the noraml force at the plank is 1375 N

c)

for computing torque about the left end

75.2 * 9.8 * (3.95/2 -x) - 3.95/2 * 1375 + 53.8 * 9.8 * 3.95 + 11.3 * 9.8 * 3.95/2 = 0

solving for x

x = 1.413 m

the position of man is 1.413 m from the pivot

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a)

let the mass of second child is m2

m2 * 9.8 * 3.95/2 - 31.3 * 9.8 * 0.91 = 0

m2 = 14.4 Kg

the mass of second child is 14.4 kg

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