Question

Compute the initial upward acceleration of a rocket of mass $\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{}\mathbf{kg}$if the initial upward force produced by its engine (the thrust) is$\mathbf{2}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{}\mathbf{}\mathbf{N}$. Do not neglect the gravitational force on the rocket.

Short answer

The initial upward acceleration of the rocket is $10\mathrm{m}/{\mathrm{s}}^2$.

Step-by-step solution

Given information

1. $m=1.3\times {10}^{4}kg$
   
2. role="math" localid="1660908233149" $T=2.6\times {10}^{5}N$
   

Understanding the concept

Acceleration of an object produced by a net force is directly proportional to the product of mass and acceleration is known as Newton’s second law of motion. So, to calculate net force use the mass of the object and acceleration of the object.

Formula

${\mathbf{F}}_{\mathbf{n}\mathbf{e}\mathbf{t}}\mathbf{=}\mathit{m}\mathbf{\times }\mathbf{a}$

Here,${\mathbf{F}}_{\mathbf{net}}$ is the force, m is the mass of the object, and a is the acceleration of the object.

Calculate the initial upward acceleration of the rocket

The net force acting on the rocket is given as,

$F_{net}=T-m\times g$

But according to Newton’s second law,

$F_{net}=m\times a$

So,

$$\begin{gathered} m\times a=T-m\times g \\ 1.3\times {10}^{4}kg\times a=2.6\times {10}^{5}N-1.3\times {10}^{4}kg\times 9.81m/s^2 \\ a=\frac{2.6\times {10}^{5}N-1.3\times {10}^{4}kg\times 9.81m/s^2}{1.3\times {10}^{4}kg} \\ =10m/s^2 \end{gathered}$$

Therefore, the initial acceleration of the rocket is $10m/s^2$.