Force & Acceleration

As stated on the previous page, 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

Newton's second law, downloadable AS & A Level Physics revision notes

Newton’s Second law equation

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 is given by either the positive or negative direction as shown in the examples below

Resultant Force horizontal, downloadable AS & A Level Physics revision notes

Resultant forces on a body

The resultant force could also be at an angle, in which case addition of vectors is used to find the magnitude and direction of the resultant force.
- For more details on this, have a look at the page on “Scalars & Vectors”

Acceleration

Given the mass, Newton’s Second Law means you can find the acceleration of an object
Since acceleration is also a vector, it can be either positive or negative depending on the direction of the resultant force
Negative acceleration is deceleration
An object may continue in the same direction however with a resultant force in the opposite direction to its motion, it will slow down and eventually come to a stop

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

The direction you consider positive is your choice, as long the signs of the numbers (positive or negative) are consistent with this throughout the questionIt is a general rule to consider the direction of motion the object is travelling in as positive. Therefore all vectors in the direction of motion will be positive and opposing vectors such as drag forces, are negative.

Force & Acceleration (CIE AS Physics)

Revision Note