Rockets

As with lifts, rockets are also examples of objects in vertical motion. The force of gravity pulls the rocket down while the thrust of the engine pushes the rocket upwards. The force that the engine exerts must overcome the force of gravity so that the rocket can accelerate upwards.

Image credit: public domain

The worked example below looks at the application of Newton's second law in launching a rocket.

Example: Newton's Second Law: Rockets

Question

A rocket (of mass $\text{5 000}$ $\text{kg}$) is launched vertically upwards into the sky at an acceleration of $\text{20}$ $\text{m·s$^{-2}$}$. If the magnitude of the force due to gravity on the rocket is $\text{49 000}$ $\text{N}$, calculate the magnitude and direction of the thrust of the rocket's engines.

Solution

Step 1: Analyse what is given and what is asked

We have the following:

$m=\text{5 000} \text{kg}$

$\vec{a}$=$\text{20}$ $\text{m·s$^{-2}$}$ upwards.

$\vec{F}_g$=$\text{49 000}$ $\text{N}$ downwards.

We are asked to find the thrust of the rocket engine $\vec{F}$.

Step 2: Find the thrust of the engine

We will apply Newton's second law: \begin{align*} \vec{F}_R & = m\vec{a}\ \text{(using signs to indicate direction)} \\ F - F_g & = (\text{5 000})(\text{20}) \\ F - (\text{49 000}) & = (\text{5 000})(\text{20}) \\ F &= \text{149 000}\text{ N} \end{align*}

Step 3: Quote your final answer

The force due to the thrust is $\text{149 000}$ $\text{N}$ upwards.

Example: Rockets

Question

How do rockets accelerate in space?

Solution

Step 1:

Gas explodes inside the rocket.
This exploding gas exerts a force on each side of the rocket(as shown in the picture below of the explosion chamber inside therocket).
Due to the symmetry of the situation, all the forces exertedon the rocket are balanced by forces on the opposite side, except for the forceopposite the open side. This force on the upper surface is unbalanced.
This is therefore the resultant force acting on the rocket and itmakes the rocket accelerate forwards.

This lesson is part of:

Newton's Laws

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