**Momentum**

Every moving object has momentum. Momentum is the tendency of a moving object to keep moving in the same direction. The formula for calculating momentum is:

**p = mv**

p = momentum (in kg·m/s)

m = mass (in kg)

v = velocity (in m/s)

**Example 1**

What is the momentum of a truck with a mass of 1200kg and moving at 60km/h?

**Step I**. Change the unit of velocity from km/h to m/s.

60km/h = 60km/h x 1h/3600s x 1000m/1km = 17m/s

**Step II**. Substitute mass and velocity into the momentum formula.

p = mv = 1200kg x 17m/s = **2.0 x 10 ^{4} kg·m/s**

**Conservation of Momentum**

When there is **no external force** acting on a the objects involved, **total momentum is conserved** and stays the same in collisions or explosions.

*Conservation of momentum questions can be challenging... But it's worth a try!!* 💪

**Example 2**

One clay dough ball with a mass of 6kg rolls to the right at 4m/s. Another clay dough ball with a mass of 4kg rolls to the left at 3m/s. After the two balls collide into each other, they stick together and roll as one ball. What is the direction and speed of the ball after collision?

**Step I**. Since there is no external force acting on the two balls, momentum is conserved.

**total momentum before collision = total momentum after collision**

**Step II**. One ball rolls to the right while the other rolls to the left, so we decide the **right direction to be positive velocity**.

**Step III**. Calculate the total momentum before collision.

momentum before collision = (6kg) x (4m/s) + (4kg) x (-3m/s) = 12kg·m/s

**Step IV**. Calculate the total momentum after collision.

After collision, one ball with a mass of 10kg rolls at v m/s.

momentum after collision = (10kg) * (v m/s) = 10v kg·m/s

**Step V**. Solve the equation.

12 = 10v

v = 1.2m/s

Because the sign of v is positive, the ball will **travel to the right at 1.2m/s.**

**Momentum and Force**

Force can be represented as the rate of change of momentum.

**F = Δp / Δt**

**Example 3**

Calculate the force needed the accelerate a toy truck of 400g from rest to 8m/s in 10 seconds.

**Step I**. Calculate the change in momentum.

**Step II**. Substitute the known values into the formula. F = (3.2 kg·m/s) / 10s =

**0.32N**

**Example 4**

Explain in the context of momentum and force why cars have airbags as a safety measure.

When an accident happens and the car suddenly brakes, there will be a huge **reduction in momentum** over a short time period. To decrease the force applied to the driver during this accident, the time for the same momentum change to happen should increase (because force is equal to the rate of change of momentum). An airbag **increases the time for the momentum change**, thereby **decreasing the force** applied on the driver. Less force on the driver means **less injuries**, so cars have airbags as a safety measure.