Physics: momentum and collisions (grade 11) · lesson

What momentum is

💡 Momentum is mass times velocity, so both mass and speed matter.

Momentum p = m × v, in kg·m/s. A 1,000 kg car at 2.0 m/s has 2,000 kg·m/s. A 50 kg runner at 8.0 m/s has only 400 kg·m/s.

Any moving object has momentum, not just objects in a collision. An object at rest has zero momentum.

🧠 Let's work it out

A 0.50 kg ball hits a wall at 6.0 m/s and stops.

Before: 0.50 × 6.0 = 3 kg·m/s.
After: 0.

What do you think comes next?

momentum: mass times velocity

🔗 Khan Academy: Force pairs and momentum · Khan Academy (free) ↗

Momentum is conserved

💡 With no outside forces, total momentum before equals total momentum after.

In any collision with no outside forces, momentum is passed between objects, but the total stays the same. This is true whether objects bounce apart or stick together.

If everything starts at rest, total momentum is zero, and it stays zero. When two skaters push apart, their momenta are equal in size and opposite in direction. The lighter one moves faster.

🧠 Let's work it out

A 2.0 kg cart at 3.0 m/s hits a 1.0 kg cart at rest and they stick.

Before: 2.0 × 3.0 = 6.
After, 3.0 kg moves together, so v = 6 ÷ 3.0 = 2 m/s.

What do you think comes next?

conserved: the total stays the same

🔗 PhET: Collision Lab · PhET Interactive Simulations (free) ↗

Force and stopping time

💡 The same change in momentum takes less force when it is spread over more time.

Change in momentum = force × time. A 200 N force for 0.30 s changes momentum by 60 kg·m/s.

In a crash, a passenger's momentum must drop to zero either way. An airbag or foam makes the stop last longer, which lowers the force. A parachute lowers the speed, so there is less momentum to stop.

🧠 How to think about it

For any safety design, ask: does it lower the momentum, or lengthen the stopping time? A stiff base does neither: it stops things fast and raises the force.

impulse: force times time; it equals the change in momentum

Force pairs

💡 When two objects push on each other, the forces are always equal in size and opposite in direction.

Newton's third law: if a truck pushes on a car, the car pushes back on the truck just as hard. Mass and speed don't make the forces unequal.

The effects can still differ. The car has less mass, so the same force changes its velocity more.

🧠 Let's work it out

Separate force from effect.
The forces are equal.
The accelerations are not, because a = F ÷ m.

What do you think comes next?