Section 4.1: Impulse
When a force acts on an object for a certain time, it changes the object’s momentum. The product of the average force and the time interval during which it acts is called impulse.
\[
J = F \Delta t
\]
where:
\( J \) = impulse (N·s),
\( F \) = average force (N),
\( \Delta t \) = time interval (s).
\( J \) = impulse (N·s),
\( F \) = average force (N),
\( \Delta t \) = time interval (s).
Impulse is also equal to the change in momentum:
\[
J = \Delta p = m v_f - m v_i
\]
Example: Impulse from a Kick
A 0.5 kg soccer ball initially at rest is kicked and leaves the foot with a velocity of 20 m/s. Find the impulse delivered to the ball.
Initial momentum: \( p_i = 0.5 \times 0 = 0 \, \text{kg·m/s} \)
Final momentum: \( p_f = 0.5 \times 20 = 10 \, \text{kg·m/s} \)
Change in momentum = \( \Delta p = p_f - p_i = 10 - 0 = 10 \, \text{N·s} \)
Impulse = 10 N·s
Practice Problems
- A 2 kg ball moving at 4 m/s is stopped by a wall in 0.2 s. Find the impulse exerted on the ball and the average force.
- A 0.15 kg baseball changes velocity from 30 m/s to 0 in 0.01 s when caught. Find the impulse and the average force exerted by the glove.
- A 1.2 kg object’s momentum changes from 6 kg·m/s to -2.4 kg·m/s. Find the impulse delivered to the object.
Key Notes
- Impulse has the same units as momentum (N·s or kg·m/s).
- A large force applied for a short time can have the same impulse as a small force applied for a long time.
- Impulse explains why seatbelts and airbags are important — they increase stopping time and reduce force on passengers.