Chapter 9, Problem 17P

Three children are trying to balance on a seesaw, which includes a fulcrum rock acting as a pivot at the center, and a very light board 3.2 m long (Fig. 9-57).Two playmates are already on either end. Boy A has a mass of 45 kg, and boy B a mass of 35 kg. Where should girl C, whose mass is 25 kg, place herself so as to balance the seesaw?

Figure 9-57

To determine

The position where girl should sit to balance the seesaw.

Answer to Problem 17P

Solution:

6.3 m to right of fulcrum rock

Explanation of Solution

Given:

Mass of boy A = 45 kg

Mass of boy B = 35 kg

Mass of girl C =25 kg

Formula used: For equilibrium:

  ${\displaystyle \sum \tau }=r_i\times F_i=0$

Here, $F_i$ is the applied force and $r_i$ represents its corresponding distance from the rotational axis.

Calculation:

Substitute the values and solve:

  $\begin{array}{l}\frac{45\text{kg}\times \text{9}\text{.8}\times \text{3}\text{.2}}{2}\text{=}\frac{\text{35}\times \text{9}\text{.8}\times \text{3}\text{.2}}{2}\text{+25}\times x\\ x=6.3\text{m}\end{array}$

Conclusion:

Thus, the girl C should place herself 6.3 m to right of fulcrum rock.