Using Newton's Laws effectively

Launching rockets

Space shuttle at launch: the thrust (T) from the rocket engines is greater than the weight (W) of the shuttle.

The lift-off of a space shuttle is an example of an unbalanced force in action. The space shuttle accelerates upwards from its launch pad. The thrust T from the rocket engines is greater than the weight W of the rocket system. Since force T is greater than the force W, the effect of one force does not cancel that of the other. The forces acting are unbalanced.

The rocket launch is a very good example to look at when considering Newton's First and Second Laws.

When preparing for launch, the rocket is stationary.

If the rocket is stationary then the forces on the rocket are balanced.

Question

What forces are acting on the rocket while waiting for lift-off?

The weight of the rocket acting downwards and the reaction force of the launcher on the rocket keeping it upright and ready to go.

Remember:

Weight = mass \times gravitational\,field\,strength

W = m \times g

(where weight ( W) is in Newtons ( N), mass ( m)is in kilograms ( kg) and gravitational field strength ( g) is in Newtons per kg ( Nkg^{-1})

When the engines are fired, an unbalanced force accelerates the rocket into the sky.

The upward force of the thrust from the rocket engines is greater than the downward weight of the rocket. This results in an unbalanced upward force, causing the rocket to accelerate upwards.

Example

Question

If the weight of the rocket is 20,000N and the thrust of the engines is 50,000N, what is the unbalanced force accelerating the rocket?

Answer

Unbalanced force= 50,000 - 20,000 = 30,000N(upward)

This unbalanced force accelerates the rocket.

This is where Newton's Second Law is applied.

Newton's Second Law states that

Unbalanced\,force = mass \times acceleration

F = m \times a

(where unbalanced force is in Newtons N), mass is in kilograms ( kg) and acceleration is in metres per second per second ( m\,s^{-2})

Example

Question

If the mass of the rocket above is 2041\, kg, what is the acceleration of the rocket at take off?

Remember, from the above question, the unbalanced force (accelerating force) is 30,000N.

Answer

F = m \times a

30000 = 2041 \times a

a \times 2041 = 30000

a = 30000 \div 2041

a = 14.7\,m\,s^{-2}

If the weight is known, then the mass can be calculated.

Look for the thrust (upward force) of the engines.

Unbalanced\,\,force=Thrust\,-\,Weight

Find the unbalanced force.

The acceleration can be calculated using  \frac{f}{m}