Question

A $\mathbf{500}\mathbf{}\mathbf{kg}$rocket sled can be accelerated at a constant rate from rest to $\mathbf{1600}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{h}$in$\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{s}$. What is the magnitude of the required net force?

Short answer

The magnitude of the required force is$1.23\times {10}^5\mathrm{N}$ .

Step-by-step solution

The given data

• Mass of the rocket,$m=500\mathrm{kg}$.
• Initial velocity of the rocket,$v_i=0\mathrm{m}/\mathrm{s}$
• Final velocity of the rocket,$v_f=1600\mathrm{km}/\mathrm{hr}or444.44\mathrm{m}/\mathrm{s}$.
• Rate of constant acceleration, $t=1.8\mathrm{s}$.

Understanding the concept of kinematics

As we are given the change in velocity in the given period, we can find the acceleration of the rocket.

We already have the mass of the rocket, using Newton’s 2nd law we can find the net force acting on it.

Formula:

Force according to Newton’s second law, $F=ma$ (i)

Acceleration of a body in motion, $a=\frac{∆V}{∆t}$ (ii)

Calculation of magnitude of the force

Using equation (i), we get the magnitude of the force on the rocket as:

$$\begin{gathered} F=500\mathrm{kg}\times \frac{444.44\mathrm{m}/\mathrm{s}}{1.8\mathrm{s}}(\because \mathrm{from}\mathrm{equation}(\mathrm{ii}),\mathrm{a}=\frac{{\mathrm{v}}_{\mathrm{f}}-{\mathrm{v}}_{\mathrm{i}}}{\mathrm{t}}) \\ =1.23\times {10}^5\mathrm{N} \end{gathered}$$

Hence, the value of force is$1.23\times {10}^5\mathrm{N}$.