Answer to Question #281263 in Physics for Reinn

Question

Consider a balanced seesaw. The balanced seesaw consists of a girl weighing 250 N on the

left side of the seesaw and a boy weighing 500 N on the right side as shown in the Figure below. The

girl on the left was given a bag of apples weighing 50 N by her mother. Where should the girl sit in

order to be in balance, assuming the heavier boy does not move? Aside from calculations, express

your answer through drawings showing a free-body diagram of forces present in the girl and boy

before and after the girl was handed a bag of apples by her mother.

Answer 1

Initially, the equilibrium of moments was

$$W_gx_1=W_bl.$$

After the girls was given apples:

$$(W_g+W_a)x_2=W_bl.$$

Divide one equation by another:

$$\frac{W_gx_1}{(W_g+W_a)x_2}=1.$$

Express x₁ and x₂ from the equations:

$$x_1=W_bl/W_g=2l,\\ x_2=W_bl/(W_g+W_a)=1.67l.$$

The girl should move closer to the boy by

$$\Delta x=x_1-x_2=2l-1.67l=0.33l,$$

where l is the length of the seesaw from the point of rotation to the point where the boy sits.