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Ch 6 - Momentum

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Ch 6 - Momentum

- Momentum = a vector quantity defined as the product of an object’s mass and velocity
- p = mv (momentum = mass x velocity)

- M = 2250 g = 2.25 kg
- V = 4 m/s
- p = mv = 2.25 x 4 = 9 kgm/s east

- A change in momentum takes force and time
- When a soccer ball is moving very fast, the player must exert a large force over a short time to change the ball’s momentum and quickly bring the ball to a stop

- Impulse = for a constant external force, the product of the force and the time over which it acts on an object; OR, the change in momentum of an object
FΔt = Δp = mvf – mvi

Impulse = change in momentum =

final momentum – initial momentum

A 1400kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30s. Find the magnitude of the force exerted on the car during the collision.

- M = 1400kg
- Δt = 0.30s
- Vi = 15 m/s west = -15 m/s
- Vf = 0 m/s
- F = ?

6.2 – Conservation of Momentum

- The total momentum is conserved
- That is, the total momentum at the beginning of the situation has to equal the total momentum at the end

- This formula can be used in lots of different examples, like collisions, explosions, or when objects push away from each other.

A 76kg boater, initially at rest in a stationary 45kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?

- The conservation of momentum fits with Newton’s Third Law
- Every action has an equal but opposite reaction

- In real life, forces during collisions are not constant
- In physics world, we will work as if we are using the “average force” in our calculations

6.3 – Elastic and Inelastic Collisions

- Perfectly Inelastic Collisions
- Two objects collide and stick together, moving together as one mass
- Momentum is Conserved

NOTE: You will get the same results using the equation we already learned for conservation of momentum. This just reminds you that the masses stuck together!

Speed of combined fish = 4 km/hr

- Kinetic Energy is NOT constant (conserved) in inelastic collisions
- When the two objects stick together, some energy is lost
- Deformation of objects (crunching of cars)
- Sound
- Heat

- When the two objects stick together, some energy is lost

Then compare the initial KE to the final KE to see how much energy was “lost”

- Elastic Collisions
- Two objects collide and then move separately
- Both Momentum and Kinetic Energy are Conserved

- In the real world, most collisions are neither elastic nor perfectly inelastic
- In physics world, we act as if they fall into one of the two categories

Perfectly Inelastic Collision

Stick together

Momentum Conserved

Kinetic Energy NOT Conserved

Elastic Collision

Bounce off

Momentum Conserved

Kinetic Energy Conserved