Question

Question: A physics Brady Bunch, whose weights in newtons are indicated in Fig.12-27, is balanced on a seesaw. What is the number of the person who causes the largest torque about the rotation axis At fulcrum fdirected (a) out of the page and (b) into the page?

Short answer

Answer:

1. Person no. 2 causes the largest torque which is directing out of page about the rotation axis at fulcrum f.
2. Person no. 7 causes the largest torque which is directing into the page about the rotation axis at fulcrum f.

Step-by-step solution

Understanding the given information

The masses of the people and distances between them.

Concept and formula used in the given question

Using the right-hand rule, you can find the direction of torque exerted by the people. Then using the formula for torque, you can find the magnitude of torques. After comparing them, you can decide which person exerts the maximum torque in each direction. The formula used is given below. $\tau =r\times F$

(a) Calculate the number of the person who causes the largest torque about the rotation axis at fulcrum f directed out of the page and  

Using right hand rule, you note that the people marked 1 to 4 exert torques which are pointing out of the page, and the people marked 5 to 8 are pointing into the page.
The torques which are pointing out of the page are,
Torque exerting on person no.1:

$$\begin{gathered} {\tau }_1=220\left(4\right)\text{sin}90° \\ =880\text{Nm} \end{gathered}$$

Torque exerting on person no.2:

$$\begin{gathered} {\tau }_2=330\left(3\right)\text{sin}90° \\ {\tau }_1=990\text{Nm} \end{gathered}$$

Torque exerting on person no.3:

$$\begin{gathered} {\tau }_3=440\left(2\right)\text{sin}90° \\ =880\text{Nm} \end{gathered}$$

Torque exerting on person no.4:

$$\begin{gathered} {\tau }_4=560\left(1\right)\text{sin}90° \\ =560\text{Nm} \end{gathered}$$

Therefore, person no.2 causes the largest torque which is directing out of page about the rotation axis at fulcrum f.

(b) Calculate the number of the person who causes the largest torque about the rotation axis at fulcrum f directed into the page 

Torque exerting on person no.5:

$$\begin{gathered} {\tau }_5=560\left(1\right)\text{sin}90° \\ =560\text{Nm} \end{gathered}$$

Torque exerting on person no.6:

$$\begin{gathered} {\tau }_6=440\left(2\right)\text{sin}90° \\ {\tau }_1=880\text{Nm} \end{gathered}$$

Torque exerting on person no.7:

$$\begin{gathered} {\tau }_7=330\left(3\right)\text{sin}90° \\ {\tau }_3=990\text{Nm} \end{gathered}$$

Torque exerting on person no.8:

$$\begin{gathered} {\tau }_8=220\left(4\right)\text{sin}90° \\ {\tau }_4=880\text{Nm} \end{gathered}$$

Therefore, the seventh person causes the largest torque which is directing out of page about the rotation axis at fulcrum f.