Hello, Can you please help with this algebra based physics question? Thanks so m

Question

Hello,

Can you please help with this algebra based physics question? Thanks so much!

A woman of mass m = 51.6 kg sits on the left end of a seesaw—a plank of length L = 3.79 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 = 75.4 kg sit if the system (seesaw plus man and woman) is to be balanced?

(b) Find the normal force exerted by the pivot if the plank has a mass of mpl = 14.0 kg.

(c) Repeat part (a), but this time compute the torques about an axis through the left end of the plank.

Suppose a 30.2-kg child sits 1.02 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

a) if system is balanced than

net torque on system = 0

so balancing torque about pivot,

((3.79/2) x 51.6 x g ) - ( d x 75.4 x g ) = 0

d = 1.30 m from pivot.

b) balancing forces,

N - (51.6 x 9.81) - (75.4 x 9.81) - (14 x 9.81) = 1383.21 N

c) torque about left end,

= ( ( 3.79/2) x 1383.21 ) - ( (3.79/2) x 14 x 9.81) - ((3.79/2 + 1.30) x 75.4 x 9.81 )

= 2621.18 - 260.26 - 2363.26 = 0

d) using torque .

net torque = ( 1.02 x 30.2 x 9.81) - (( 3.79/ 2) x m x 9.81) = 0

m = 16.25 kg

b) N = 14g + 16.25g + 30.2g = 593.01 N

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