Section 4.2: Momentum
Momentum is a measure of the motion of an object. It depends on both the object’s mass and velocity. Momentum is a vector quantity, meaning it has both magnitude and direction.
\( p \) = momentum (kg·m/s)
\( m \) = mass (kg)
\( v \) = velocity (m/s)
The greater the mass or velocity of an object, the greater its momentum. Momentum plays a key role in collisions and impacts.
Example: Momentum of a Truck
A truck of mass 3000 kg moves at 15 m/s. Find its momentum.
\( p = m v = 3000 \times 15 = 45{,}000 \, \text{kg·m/s} \)
The truck’s momentum is 45,000 kg·m/s.
Example: Comparing Momentum
A 60 kg sprinter runs at 10 m/s. Compare the sprinter’s momentum with that of a 1,200 kg car moving at 0.5 m/s.
Sprinter: \( p = 60 \times 10 = 600 \, \text{kg·m/s} \)
Car: \( p = 1200 \times 0.5 = 600 \, \text{kg·m/s} \)
The sprinter and the car have the same momentum!
Practice Problems
- A 2 kg ball is moving at 12 m/s. Find its momentum.
- A 0.15 kg baseball has a momentum of 4.5 kg·m/s. Find its velocity.
- Which has more momentum: a 1,000 kg car moving at 3 m/s or a 100 kg cart moving at 25 m/s?
- A 70 kg runner moves at 8 m/s. Find the runner’s momentum.
- If a train car of mass 20,000 kg has a momentum of 100,000 kg·m/s, what is its velocity?
Key Notes
- Momentum depends directly on both mass and velocity.
- Momentum is always in the same direction as velocity.
- Momentum conservation will be studied in more detail later in this chapter.