Section 4.3: Impulse
Impulse measures the effect of a force applied over a time interval on an object's momentum.
Impulse:
\( \vec{J} = \vec{F} \Delta t = \Delta \vec{p} \)
- \( \vec{F} \): Average force applied
- \( \Delta t \): Time interval of force application
- \( \Delta \vec{p} \): Change in momentum
Example 1
A 10 N force acts on a 2 kg object for 3 s. Find the impulse and change in momentum.
\( J = F \Delta t = 10 \times 3 = 30 \, \text{N·s} \)
\( \Delta p = J = 30 \, \text{kg·m/s} \)
Example 2
A baseball of mass 0.15 kg moving at 40 m/s is stopped by a bat in 0.01 s. Find the average force.
\( J = \Delta p = m \Delta v = 0.15 \times 40 = 6 \, \text{kg·m/s} \)
\( F_{\text{avg}} = J / \Delta t = 6 / 0.01 = 600 \, \text{N} \)
Practice Problems
- A 3 kg object is pushed with 12 N for 4 s. Find impulse.
- A 5 kg object changes velocity from 2 m/s to 8 m/s. Find impulse.
- A ball of mass 0.2 kg is hit, changing speed from 10 m/s to -10 m/s in 0.05 s. Find average force.
- A 6 kg crate is acted on by 18 N for 2 s. Determine change in momentum.
- A 10 kg particle at rest is pushed to 5 m/s in 1 s. Find impulse and force.