Mother and father support the child sitting on the 3.80 m long plank. The weight

Question

Mother and father support the child sitting on the 3.80 m long plank. The weight of the child is 37.0 M. Table the plank to be weightless. If x = 2.20 m. what forces must the parents exert? Consider the axis of rotation to be at the RIGHT end of the plank. Repeat the previous part, but consider the axis of rotation to be at the position. Suppose, instead, that the uniform plank is NOT weightless but has a weight of 44.0 N. Take x = 1.50 m. Pick your own pick your own axis rotation and find the forces exerted by the parents. Where must the child sit to make one parent lift twice as hard as the other?

Explanation / Answer

Let Fm and Ff are the forces exerted by mother and father.

A)

1) as the plank is in equilibrium, net force and net torque acting on the plank must be zero.

Apply, net torque about right end = 0

37*(3.8 - 2.2) - Fm*3.8 = 0

Fm = 37*1.6/3.8

= 15.58 N

2) Apply, net torque about left end = 0

37*2.2 - Ff*3.8 = 0

Ff = 37*2.2/3.8

= 21.42 N

B)

1)
Apply, net torque about right end = 0

37*(3.8 - 1.6) + 44*1.9 - Fm*3.8 = 0

Fm = (37*2.2 + 44*1.9)/3.8

= 43.4 N

Apply, net torque about left end = 0

37*1.6 + 44*1.9 - Ff*3.8 = 0

Ff = (37*1.6 + 44*1.9)/3.8

= 37.6 N

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