Force & Momentum

Newton's second law is defined by the equation:

$F = m a$

Momentum is calculated using the equation:

$p = m v$

Combing these equations gives Newton's second law in terms of momentum:

$force = \frac{change in momentum}{time}$

Force is the resultant or unbalanced force measured in newtons (N)
- It is also defined as the rate of change of momentum on a body
- Where the rate of change describes how a variable changes with respect to time

Change in momentum is measured in (kg m/s)
- Change in momentum = final momentum − initial momentum

Time is how long the impact lasts and is measured in seconds (s)
- The shorter the time over which momentum changes then the bigger the force applied and vice versa
- So, force and time are inversely proportional to each other

Remember to consider the direction of object motion
- If you take the initial direction as positive then the reverse direction is negative

Worked example

A car of mass 1500 kg hits a wall at an initial velocity of 15 m/s and rebounds with a velocity of 5 m/s. The car is in contact with the wall for 3 seconds.

Calculate the average force experienced by the car and state the direction of the force.

Answer:

Step 1: List the known quantities

Mass of car, m = 1500 kg
Velocity before collision = 15 m/s
Velocity after collision = 5 m/s
Time of impact = 3 s

Step 2: Draw a diagram of the collision

The diagram should include:
- The velocity before and after the collision
- The direction of motion before and after the collision

2-4-we-solution-diagram

Step 3: Calculate the initial momentum of the car

p = mv

initial momentum = 1500 × 15

initial momentum = 22 500 kg m/s

Step 4: Calculate the final momentum of the car

p = mv

final momentum = 1500 × −5

final momentum = −7500 kg m/s

Step 5: Calculate the change in momentum before and after the collision

change in momentum = final momentum − initial momentum

change in momentum = −7500 − (22 500)

change in momentum = −30 000 kg m/s

Step 6: Calculate the force on the car and state the direction

$force = \frac{change in momentum}{time}$

$force = \frac{- 30 000}{3}$

$force = - 10 000 N$

The minus sign means the direction of the force is to the left or in the opposite direction to the car's initial motion

Worked example

A tennis ball hits a racket twice, with a change in momentum of 0.5 kg m/s both times.

During the first hit, the contact time is 2 s and during the second hit, the contact time is 0.1 s

Determine which tennis racket experiences the greatest force from the tennis ball.

2-4-we-different-contact-times

Answer:

Step 1: Calculate the force during the first hit

$force = \frac{change in momentum}{time}$

$force = \frac{0.5}{2}$

$force = 0.25 N$

Step 2: Calculate the force during the second hit

$force = \frac{change in momentum}{time}$

$force = \frac{0.5}{0.1}$

$force = 5.0 N$

Step 3: State your answer

The tennis racket experiences the greatest force from the ball during the second hit

Force & Momentum (WJEC GCSE Physics)

Revision Note

Force & Momentum

Worked example

Worked example

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Author: Ann H