Chapter 11, Problem 4A

For two kids of different masses balancing on a seesaw, should the heavier kid sit closer or farther from the fulcrum compared with the lighter kid?

To determine

The place where the heavier kid must sit from the fulcrum on the seesaw in order to balance it.

Answer to Problem 4A

Closer to the fulcrum as compared to the lighter kid.

Explanation of Solution

Introduction:

The torque acting about an axis of rotation due to the force $F$ is given by,

  $\begin{array}{c}\tau =F\times \left(r\right)\\ =F\text{r}\sin \theta \end{array}$

Where,

  $r=$ denotes the shortest distance of the point of application of force from the axis of rotation.

  $\theta =$ angle between the force and the distance

When the kids sat on the seesaw, their weight acts in downward direction. Hence, the angle between the distance and the force on the kids is $90°$ .

Now, in order to balance the seesaw, the torque exerted on the seesaw due to weight of the kids must be equal.

  $\begin{array}{c}{W}_l{r}_l=W_h{r}_h\\ \frac{W_h}{W_l}=\frac{r_l}{r_h}\end{array}$

Since,

  $\begin{array}{l}\frac{W_h}{W_l}>1\\ \Rightarrow \frac{r_l}{r_h}>1\\ \Rightarrow r_l>r_h\end{array}$

Conclusion:

Hence, the distance of the heavier kid from the fulcrum must be less than that of the lighter kid from the fulcrum.