Question

(i) Explain Newton's second law of motion.
(ii) A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes.

Answer 1

(i) Newton's second law explains that when a force is applied to a body, it changes the momentum of the body i.e. It changes the state of motion or of rest of the body. The rate of change of momentum of the body is directly proportional to the force applied to the body. If we increase the value of the force, it will create more change in the momentum of the body.

The mathematical form of Newton's second law,

$$\begin{gathered} \frac{dp}{dt}\propto F\Rightarrow \frac{{\displaystyle d\left(mv\right)}}{{\displaystyle dt}}\propto F\Rightarrow m\frac{{\displaystyle dv}}{{\displaystyle dt}}\propto F \\ \Rightarrow ma\propto F \end{gathered}$$

(ii) Initial velocity of the truck = 0 m/s

Distance travelled by truck in coming down the hill = 400 m

Time taken by the truck = 20 s

Let the acceleration of the truck = a

Using the second equation of motion, we can write, $s=ut+\frac{1}{2}a{t}^2$

$$\begin{gathered} \therefore 400\mathrm{m}=0+\frac{1}{2}\times \mathrm{a}\times (20\mathrm{s}{)}^2 \\ \Rightarrow \mathrm{a}=\frac{400\mathrm{m}}{200{\mathrm{s}}^2}=2\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Mass of the body = 7 metric tons = 1000 kg

Force acting on the body = $\mathrm{Mass}\times \mathrm{Acceleration}=1000\mathrm{kg}\times 2\mathrm{m}/{\mathrm{s}}^2=2000\mathrm{N}$