Chapter 6, Problem 6A

If the mass of a sliding block is tripled at the same time the net force on it is tripled, how does the resulting acceleration compare with the original acceleration?

To determine

To explain: Effect on resulting acceleration as compared to the original acceleration.

Answer to Problem 6A

The resulting acceleration remains the same, $a\text{'}=a$ .

Explanation of Solution

Given:

Mass of the sliding box is tripled.

Force on the sliding block is also tripled.

Formula Used:

From Newton’s second law, the net force is given as

  $F=ma$

Where, $m$ is mass of object and $a$ is acceleration.

Calculation:

Let, the original force on the block is F , mass of the block is m and acceleration is a ,

Force on the block is tripled so, $F\text{'}=3F$

Mass of the block is also tripled so, $m\text{'}=3m$

Now,

  $\begin{array}{l}F\text{'}=m\text{'}a\text{'}\\ \Rightarrow 3F=3m\times a\text{'}\\ \Rightarrow a\text{'}=\frac{3F}{3m}=a\\ \text{So, }a\text{'}=a\end{array}$

Conclusion:

Therefore, the resulting acceleration remains the same that is $a\text{'}=a$ .