Force & Momentum (WJEC GCSE Physics): Revision Note

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

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

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

$\mathrm{force}=\frac{-30000}{3}$

$\mathrm{force}=-10000\mathrm{N}$

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

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 strike of the tennis racket experiences the greatest force from the tennis ball.

Answer:

Step 1: Calculate the force during the first hit

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

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

$\mathrm{force}=0.25\mathrm{N}$

Step 2: Calculate the force during the second hit

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

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

$\mathrm{force}=5.0\mathrm{N}$

Step 3: State your answer

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