Chapter 4.1, Problem 15SSC

To determine

Masses of the two blocks

Explanation of Solution

Given:

Horizontal force is given 1 N and acceleration of first block is 3 times less than first like.

Horizontal force is given 1N

Let mass of the first block is $m_1\text{ kg}$

And acceleration of the first block is $a_1=a{\text{ m/s}}^2$

According to Newton’s law horizontal force is given by,

  $F=ma$

Therefore,

  $\begin{array}{l}1=m_{1}a\\ m_1=\frac{1}{a}\text{ kg}\end{array}$

Now, in second case acceleration of the block is $a_2=3a{\text{ m/s}}^2$

Let mass of the second block be $m_2\text{ kg}$

Therefore,

  $\begin{array}{c}1=3a\times m_2\\ m_2=\frac{1}{3a}\\ =\frac{1}{3}{m}_1\end{array}$

Conclusion:

Therefore,the mass of the first block is 3 times the mass of second block.