Momentum

Momentum

INERTIA

The property of an object (matter) by which it either continues to stay at rest (not move) or continues at the same speed (uniform motion) in a straight line - unless an external force acts on it.

MOMENTUM

Rules of momentum

• momentum is always conserved (saved)

• Momentum depends upon the mass and velocity of an object

• p = M x V

• Kg m/s

Simple momentum questions

• .A car of mass 1000kg travelling at a velocity of 15 m/s?

• A horse of mass 500kg running at a velocity of 20 m/s?

• .A car of mass 1000kg with a momentum of 15,000 kg m/s?

• .A person of mass 75kg with a momentum of 112.5 kg m/s?

Conservation of momentum

• As long as there are no external forces acting on the objects then momentum will always be conserved in a collision. 

• Total momentum before a collision = 0

  Total momentum after a collision = 0

Two trains

Train 1: Mass (M1) of 12000 Kg, travelling at a Velocity (V1) of 5 m/s

Train 2: Mass (M1) of 12000 Kg and is at rest (V2) = 0

Train 1 crashes into Train 2

What is the Velocity of both trains after the crash?

(V2)

Momentum is conserved !

• Firstly: work out the total momentum before the crash.

• = (m1 x v1 ) + (m2 x v2 )

• = (12,000 x 5) + (12,000 x 0)

• = 60,000 + 0

• = 60,000 kg m/s

Momentum is conserved !

• Secondly: work out the total momentum after the crash.

• = (m1 x v1 )  + (m2 x v2 )

• = (12,000 x 0) + (12,000 x v2 )

• = 0 + (12,000 x v2 )

• = 12,000 x v2

• S0................

60,000 = 12,000 x v2 

p = M x V

• Rearrange to find Velocity - V = p / M

• V2  = 60,000 / 12,000 

• V2  = 5 m/s

Your Turn

• A bullet of mass 10g is fired from a 6kg rifle at a speed of 300m/s. What is the recoil velocity of the rifle?

The Steps (remember to check all units)

• Momentum before = 0

• Momentum after firing = momentum bullet + momentum rifle = 0

• p= M x V + M x V

What you should have so far....

• p = M xV + M x V

• p = 0.01 x 300 + 6 + 0

• p = 3 Kg m/s

• Now find the Velocity of the rifles recoil - the rifle and the bullet now have a combined mass!!

Momentum is conserved.

• Momentum before a collision must be the same as momentum after a collision

• This only applies to closed systems (no external force is acting on the objects)

• Momentum has a + or - direction

Slightly trickier question

• A trolley of mass 4kg moving at 10 m/s collides with a 2 kg trolley moving in the same direction at a velocity of 4m/s. they separate after the collision and the 4 kg trolley slows to 7m/s. What is the final speed of the other trolley?

• DRAW THIS OUT AS WE GO THROUGH IT

Step 1

• Work out the momentum of each trolley

• p= M1 x V1

• p = M2 x V2

Step 2: The Crash! (trolleys are now one system travelling in the SAME direction)

• What is the combined momentum of the trolleys?

Step 3: New speed of trolley 1, what is its new momentum?

• p = M x V

Step 4: What is the new momentum of trolley 2?

• Remember that total momentum MUST BE CONSERVED

• The new Momentum of trolley 1 is 28 Kg m/s

• What must the new momentum of trolley 2 be?

Step 5: What is the new Velocity of trolley 2?

• V = p/M

External forces

• When a force is applied to an object, the velocity of that object will change.

• This means that the momentum will also change

• The change of momentum depends upon the size of the force and the length of time that force was applied for.

Change in momentum.

• Change in momentum = Force x time

• Δp = F x t

• REMEMBER

• p = M x V

• Change in momentum = p2 - p1

Question 1

• A rugby ball of mass of 0.5 Kg is kicked from stationary to a velocity of 8 m/s. The kickers foot is in contact with the ball for 0.1 seconds.

• What force does the kicker use?

Question 1: Answer

• F = Δp / t

• F = (0.5 x 8) - (0.5 x 0) = 4

• 4/0.1

• Force = 40 N

One more for you!

• A tennis ball is rolled at a toy car of a mass 0.1 Kg. The car is moved with a velocity of 0.5 m/s

• If the car and the ball are in contact for 0.01 seconds, what Force was the balled rolled with?

Work through of question 2.

• F = Δp / t

• F = (0.1 x 0.5) - (0.1 x 0) = 0.05

• 0.05 / 0.01

• Force = 5 Newton