Force & Acceleration

Newton's second law of motion tells us that objects will accelerate if there is a resultant force acting upon them
This acceleration will be in the same direction as this resultant force

$F = m a$

Where:
- F = force in newtons (N)
- m = mass in kilograms (kg)
- a = acceleration in metres per second squared (m s^-2)

Resultant force

Since force is a vector, every force on a body has a magnitude and direction
The resultant force is therefore the vector sum of all the forces acting on the body
The direction of the force is indicated as either positive or negative

Resultant forces on a body

4-4-newtons-2nd-law-example-calcs

Resultant forces on a body are indicated by a positive or negative value

The resultant force could also be at an angle, in which case vector addition is used to find the magnitude and direction of the resultant force.
- More details on vector addition can be found in Scalars & Vectors

Acceleration

Newton’s second law can be used to find the acceleration of an object of a known mass
Since acceleration is also a vector, it can be either positive or negative depending on the direction of the resultant force
An object will speed up (positive acceleration) if the resultant force acts in the same direction as the direction of motion
An object will slow down (negative acceleration) if the resultant force acts in the opposite direction to the direction of motion
The acceleration will always be in the same direction as the resultant force

Worked example

A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.

(a)

When in flight, the force due to air resistance is 500 kN.

Calculate the resultant force on the rocket.

(b)

The mass of the rocket is 0.8 × 10⁵ kg.

Calculate the acceleration of the rocket and state the direction of the acceleration.

Answer:

(a)

Step 1: Sketch a diagram of the forces acting on the rocket

3-1-2-we-forces-diagram-rocket-cie-new

Step 2: Convert all the forces into SI units (newtons)

Upward acting force (positive direction):
- Thrust = 15 MN = $15 \times 10^{6} N$
Downward acting forces (negative direction):
- Weight = 8 MN = $8 \times 10^{6} N$
- Air resistance = 500 kN = $500 \times 10^{3} N$

Step 3: Calculate the resultant force acting on the rocket

$F = (15 \times 10^{6}) - (8 \times 10^{6}) - (500 \times 10^{3})$

$F = 6.5 \times 10^{6} N upwards$

(b)

Step 1: List the known quantities

Force, F = 6.5×10⁶ N
Mass, m = 0.8 × 10⁵ kg

Step 2: State the equation for Newton's Second Law of motion

$F = m a$

Step 3: Rearrange to make acceleration the subject

$a = \frac{F}{m}$

Step 4: Substitute in the known values and calculate the acceleration

$a = \frac{6.5 \times 10^{6}}{0.8 \times 10^{5}}$

$a = 81 m s^{- 2}$

Step 5: State the direction of the acceleration

$a = 81 m s^{- 2} Upwards$

Remember that acceleration is always in the same direction as the resultant force

Examiner Tip

You can choose which direction is positive as long as you are consistent throughout your calculation. However, the general convention is for the direction of motion to be the positive direction.

Force & Acceleration (CIE A Level Physics)

Revision Note