Chapter 6, Problem 61A

If a loaded truck that can accelerate at $1{\text{ m/s}}^{\text{2}}$ loses its load and has three-fourths of its original mass, what acceleration can it attain if the same driving force acts on it?

To determine

Acceleration attained by the truck.

Answer to Problem 61A

The resulting acceleration of the truck is $a\text{'}=1.33{\text{m/s}}^2$ .

Explanation of Solution

Given:

Original acceleration of truck, $a=1{\text{m/s}}^2$

Driving force remains the same.

After truck losses weight, mass of the truck is three-fourth of its original mass.

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 initial driving force is F , mass of the block is m and acceleration is a ,

Driving force remains the same, $F\text{'}=F$

New mass of the truck, $m\text{'}=\frac{3}{4}m$

Now,

  $\begin{array}{l}F\text{'}=m\text{'}a\text{'}\\ \Rightarrow F=\frac{3}{4}m\times a\text{'}\\ \Rightarrow a\text{'}=\frac{4}{3}.\frac{F}{m}=\frac{4}{3}.a\\ \Rightarrow a\text{'}=\frac{4}{3}\times 1=\frac{4}{3}{\text{m/s}}^2\\ \Rightarrow a\text{'}=1.33{\text{m/s}}^2\end{array}$

Conclusion:

Therefore, the resulting acceleration of the truck is $a\text{'}=1.33{\text{m/s}}^2$ .