Chapter 7, Problem 55A

Two blocks, one three times as massive as the other, are connected by a compressed spring. When the spring is released, both blocks fly apart. Relative to the acceleration of the heavier block, what is the acceleration of the lighter block?

To determine

The acceleration of lighter block relative to the acceleration of the heavierblock.

Explanation of Solution

Given:

Let the mass of the lighter block be m , then mass of heavier block would be $m\text{'}=3m$ .

Formula Used:

Newton’s Second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is the mass a is the acceleration .

Calculation:

The two blocks are connected with the same spring. When the spring would be released, equal and opposite force would be experienced by each block. If acceleration of heavier block is a’ , then acceleration of the lighter block would be:

  $\begin{array}{l}ma=m\text{'}a\text{'}\\ ma=\left(3m\right)a\text{'}\\ a=3a\text{'}\end{array}$

Conclusion:

The acceleration of the lighter block would be three times the acceleration of the heavier block.