Two people carry a heavy electric motor by placing it on a light board 2.90m lon

Question

Two people carry a heavy electric motor by placing it on a light board 2.90m long. One person lifts at one end with a force of 370N , and the other lifts the opposite end with a force of 610N . I have gotten all of the parts right except for part D. That's all I need help with.

A)What is the weight of the motor?

B)Where along the board is its center of gravity located?

C)Suppose the board is not light but weighs 210N , with its center of gravity at its center, and the two people each exert the same forces as before. What is the weight of the motor in this case?

D)Where is its center of gravity located?

Explanation / Answer

A) Weight of motor = 370+610 = 980N

B) Let distace of center of gravity from 370N end = 'x'm
At center of gravity, torque due to gravity will be zero
By torque balance about center of gravity,
370x = 610(2.9 - x)
370x = 1769 - 610x
980x = 1769
x = 1.8
Hence center of gravity is at 1.8m from 370N end of the board

C) weight of motor = 370+610-210 = 770N

D) Let distace of center of gravity from 370N end = 'x'm
At center of gravity, torque due to gravity will be zero
By torque balance about center of gravity,
370x = 610(2.9 - x)
370x = 1769 - 610x
980x = 1769
x = 1.8
Hence center of gravity is at 1.8m from 370N end of the board

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