Question

A truck of mass $M$ is moved under a force $F$. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?

Answer 1

Step 1: Given

Mass of the truck = $M$

Driving force = $F$

Let acceleration be $a_1$

After loading mass of truck = $2M$

After loading driving force = $\frac{F}{2}$

Let acceleration be $a_2$

Step 2: Formula used

We know that

$F=ma$

Step 3: Calculating change in acceleration

Before loading

$$\begin{gathered} F=M{a}_1 \\ {a}_1=\frac{F}{M} \end{gathered}$$

After loading

$$\begin{gathered} \frac{F}{2}=2M{a}_2 \\ {a}_2=\frac{F}{4M} \end{gathered}$$

Ratio of accelerations is

$$\begin{gathered} \frac{a_1}{a_2}=\frac{{\displaystyle \raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$M$}\right.}}{{\displaystyle \raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$4M$}\right.}} \\ \frac{a_1}{a_2}=4 \\ {a}_2=\frac{a_1}{4} \end{gathered}$$

Hence, acceleration after loading the object becomes $\frac{1}{4}$ the initial acceleration.