Section 1 of 6Impulse and Momentum Change
A large impulse is needed to change the motion of a heavy or fast-moving object.
Definition
- Impulse is the product of the force acting on an object and the time for which the force acts.
Equation
- Impulse = FΔt, measured in newton seconds (N s).
Impulse theorem
- The impulse of the resultant force equals the change in momentum of the object, FΔt = Δp.
Origin
- The relationship comes from rearranging Newton’s second law in the form F = Δp/Δt.
Average force
- For a short collision the force varies, and the equation gives the average force over the contact time.
Section 2 of 6Calculating an Impulse
Collision problems follow a short routine.
1
Choose a positive direction and state the initial and final velocities of the object with signs.
2
Calculate the change in momentum, Δp = m(v − u), taking care when the object reverses direction.
3
Equate this change in momentum to the impulse of the resultant force.
4
If the contact time is known, divide the impulse by the time to find the average force.
5
State the direction of the force, which matches the direction of the change in momentum.
Section 3 of 6Controlling the Force
Controlling the Force
Same impulse
- If the change in momentum is fixed, a longer contact time gives a smaller average force.
Air bags
- An air bag lengthens the time over which a passenger is stopped, which lowers the force on their body.
Crumple zones
- A car front deforms during a crash, extending the stopping time and lowering the peak force.
Rebounds
- A ball that bounces back has a larger momentum change than one that stops, so the impulse and force are larger.
Section 4 of 6Examples
Cricket catch
- Drawing the hands back on catching extends the contact time, reducing the force on the fingers.
Landing
- Bending the knees when landing increases the time to stop, so the force on the legs is smaller.
Hitting a ball
- A bat and ball are in contact for only a few milliseconds, so the forces involved reach hundreds of newtons.
Section 5 of 6Worked Example
Question
- A tennis ball of mass 0.057 kg, initially at rest, is struck and leaves the racket at 45 m s⁻¹.
- The contact lasts 5.0 ms.
- Find the impulse and the average force.
- Change in momentum = 0.057 × 45 − 0 = 2.57 N s, so the impulse is 2.57 N s.
- Contact time = 5.0 ms = 5.0 × 10⁻³ s.
- F = impulse / time = 2.565 / (5.0 × 10⁻³) = 513 N.
Answer
- Impulse = 2.6 N s;
- average force = 5.1 × 10² N.
Section 6 of 6Exam Checklist & Tips
3.8.3 – Key Points for the Exam
- Impulse Force multiplied by the time for which it acts, equal to change in momentum.
- Contact time The duration for which two objects exert forces on each other during a collision.
- Average force The constant force that would produce the same impulse over the same time.
- Crumple zone A structure designed to deform in a collision and increase the stopping time.
Common Mistakes
- Using time in milliseconds without converting to seconds.
- Forgetting that a rebound reverses the velocity, so the change in momentum is larger than for stopping.
- Claiming that an air bag reduces the impulse; it reduces the force by increasing the time.
- Writing the unit of impulse as N m, which is a unit of energy.