Two people carry a heavy electric motor by placing it on a lightboard 4.00 m lon

Question

Two people carry a heavy electric motor by placing it on a lightboard 4.00 m long. One person lifts at oneend with a force of 100 N, and the otherlifts the opposite end with a force of 700N. (a)What is the weight of the motor?
1 N

Where along the board is its center of gravity located?
2 m (from the end where the 100 N force is applied)

(b)Suppose the board is not light but weighs 200 N, with its centerof gravity at its center, and the two people exert the same forceas before. What is the weight of the motor in this case?
3 N

Where is its center of gravity located?
4 m (from the end where the 100 N force is applied) (a)What is the weight of the motor?
1 N

Where along the board is its center of gravity located?
2 m (from the end where the 100 N force is applied)

(b)Suppose the board is not light but weighs 200 N, with its centerof gravity at its center, and the two people exert the same forceas before. What is the weight of the motor in this case?
3 N

Where is its center of gravity located?
4 m (from the end where the 100 N force is applied)

Explanation / Answer

(a) weight of motor = 100 + 700 = 800 N . distance from the 100 N end is    x.    Distance from other end is   4 -x. .    the distances are inversely proportional to theforces, i.e. bigger force is closer to the center of gravity,so: .           (4 - x)/ x    = 100 / 700 .            4 - x = (1/7)x                     x = 3.500 m    is the distance from the 100 Nend. . (b)    Now,   weight of motor = 800 - 200 =   600 N . The center of gravity is still    3.500 m from the 100 N end,because the balance of the support forces did not change. . The center of gravity is still    3.500 m from the 100 N end,because the balance of the support forces did not change.

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