Chapter 6, Problem 56A

A net force on a 2-kg cart accelerates the cart at $3{\text{ m/s}}^{\text{2}}$. How much acceleration will the same net force produce on a 4-kg cart?

To determine

Acceleration produced by same force.

Answer to Problem 56A

  $a\text{'}=1.5{\text{m/s}}^2$

Explanation of Solution

Given:

Mass of first cart, $m=2\text{kg}$

Mass of second cart, $m\text{'}=4\text{kg}$

Initial acceleration of the cart, $a=3{\text{m/s}}^2$

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

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 new acceleration is $a\text{'}$ and force new force $F\text{'}=F$

Now, initially

  $\begin{array}{l}F=ma\\ \Rightarrow F=2\times 3\\ =6\text{N}\end{array}$

Now, for mass $m\text{'}=4\text{kg}$ and $F\text{'}=F=6\text{N}$

  $\begin{array}{l}F\text{'}=m\text{'}a\text{'}\\ \Rightarrow 6=4\times a\text{'}\\ \Rightarrow a\text{'}=\frac{6}{4}=1.5{\text{m/s}}^2\end{array}$

Conclusion:

Therefore, the acceleration produced by same net force on 4 kg cart is $a\text{'}=1.5{\text{m/s}}^2$ .