Question

A child is holding up a 12 kg book at the end of their 0.5 meterlong arm. Their arm has a mass of 7 kg. How much totalupwards torque must the student's shoulder generate in order tohold both the book and arm upward? Show all your work.

Answer 1

Given:

The mass of the book, M=12 kg

The mass of the arm, m=7 kg

The length of the arm of the child, l=0.5 m

To find:

The torque generated by the arm of the child.

Step-by-step explanation:

Let us assume that the center of mass of the arm is at the middle of the length of the arm.

The downward torque applied by the arm and the book is given by,

`\begin{gathered} \tau=Ml+m*(l)/(2) \\ =l(M+(m)/(2)) \end{gathered}`

On substituting the known values,

`\begin{gathered} \tau=0.5*(12+(7)/(2)) \\ =7.75\text{ Nm} \end{gathered}`

In order to hold the book and arm up, the shoulder should generate a torque equal to the torque generated by the book and the arm but in the opposite direction.

Final answer:

Thus the upward torque that the shoulder must generate is 7.75 Nm