34. Momentum (Part 1) - Conservation of Momentum

1. What is Momentum?

• Definition: Momentum is a property possessed by all moving objects.

• The Equation:

  \text{Momentum} (p) = \text{Mass} (m) \times \text{Velocity} (v)

  • Momentum (p): Measured in kg m/s.

  • Mass (m): Measured in kg.

  • Velocity (v): Measured in m/s.

• Vector Quantity: Momentum has both magnitude and direction. If movement to the right is positive, movement to the left must be treated as negative.

2. Conservation of Momentum

In a closed system, the total momentum before an event (like a collision or an explosion) is exactly the same as the total momentum after the event.

\text{Total Momentum Before} = \text{Total Momentum After}

Collision Example (Dinosaur vs. Car)

• If a dinosaur (positive momentum) and a car (negative momentum) collide and move together:

  1. Calculate individual momenta.

  2. Add them to find the Total Initial Momentum.

  3. The combined object will have this same total momentum.

  4. To find the new velocity, divide the total momentum by the combined mass of both objects.

3. Momentum in Explosions and Recoil

If the initial momentum is zero (objects are stationary), the total momentum after the event must also be zero.

Recoil Example (Gun and Bullet)

• Before firing, the gun and bullet are stationary ($\text{Momentum} = 0$).

• After firing:

  • The bullet moves forward with positive momentum.

  • The gun must move backward (recoil) with an equal negative momentum.

  • Added together, the total remains zero.

• Calculation: Mass\left(gun\right)\cdot Velocity\left(gun\right)+Mass\left(Bullet\right)\cdot Velocity\left(Bullet\right)=0

4. Summary Table

5. Key Points to Remember

• Always convert mass to kilograms (kg) (e.g., 5g = 0.005kg).

• Assign a direction (positive or negative) to velocities and keep them consistent.

• For combined objects after a collision, use their total mass in the p = mv formula.