Question

What force should an engine develop, if it causes the displacement of a vehicle through $100m$, such that work done is one mega joule?

Answer 1

Step 1: Given data

Work done by the engine $\left(W\right)$=$1$mega joule

Displacement by the engine $\left(s\right)=100m$

Force $\left(F\right)=?$

Step 2: Conversion of a unit of work and mass

The bigger unit of work is Mega joule

$$\begin{gathered} 1megajoule={10}^{6}Joule \\ 1MJ={10}^{6}J \end{gathered}$$

The bigger unit of mass is Ton

$$\begin{gathered} 1Ton=1000kg \\ 1T=1000kg \end{gathered}$$

Step 3: Formula used

According to the formula of work

$$\begin{gathered} Work=force\times displacement \\ Force=\frac{Work}{displacement} \\ F=\frac{W}{s}........\left(a\right) \end{gathered}$$

According to the formula of force

$$\begin{gathered} Force=mass\times acceleration \\ F=ma \\ a=\frac{F}{m}........\left(b\right) \end{gathered}$$

Step 4: Calculating the force

On, putting the value on equation (a), we get

$F=\frac{W}{s}=\frac{{10}^{6}J}{100m}={10}^{4}N$

Hence, the force will be $F={10}^{4}N.$

Step 5: Calculating the acceleration

On, putting all the given values in equation (b), we get

$a=\frac{F}{m}=\frac{{10}^{4}N}{1000kg}=10m/s^2$

Hence, the acceleration will be $a=10m/s^2.$