Chapter 7, Problem 59P

To determine

The CM of the mallet above the bottom of handle.

Answer to Problem 59P

The CM of the mallet above the bottom of handle is $0.248\text{m}$ .

Explanation of Solution

Given:

The mass of the cylindrical head is $m_1=2.00\text{ kg}$ .

The mass of the cylindrical handle is $m_2=0.500\text{ kg}$ .

The length of the handle is $l=0.240\text{ m}$ .

The diameter of the head is $d=0.0800\text{ m}$ .

Formula used:

The expression for the distance of CM $\left(x_{CM}\right)$ is,

  $x_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Here, $m_1$ is the mass of the object 1, $m_2$ is the mass of object 2, $x_1$ is the distance of object 1 from the origin along x direction, and $x_2$ is the distance of object 2 from the origin along x direction.

Calculation:

The distance of CM along x axis is,

  $\begin{array}{l}{x}_{\text{CM}}=\frac{m_1\left(l+\frac{d}{2}\right)+m_2\frac{l}{2}}{m_1+m_2}\\ x_{\text{CM}}=\frac{\left(\text{2}\text{.00 kg}\right)\left(\text{0}\text{.24 m}+\frac{0.08\text{ m}}{2}\right)+\left(\text{0}\text{.500 kg}\right)\left(\frac{0.24\text{ m}}{2}\right)}{\left(\text{2}\text{.00 kg}\right)+\left(\text{0}\text{.500 kg}\right)}\\ x_{\text{CM}}=0.248\text{ m}\end{array}$

Conclusion:

Thus, the CM of the mallet above the bottom of handle is $0.248\text{m}$ .