Momentum 2

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Momentum 2
Change in Momentum (Δp)
When an object’s velocity changes, obviously the momentum changes as well.
We are often required to calculate the Change in Momentum.
To do this we use a formula :
Δp = m(v – u)

Δp is the “Change in Momentum”
m is the mass
v is the final velocity
u is the initial velocity

Examples
It is best to learn by doing some examples.
1. A 2kg trolley is moving at 3ms^-1 east. Then the velocity is changed to 8ms^-1 east. Calculate the change in momentum.
Δp = m(v – u)
Δp = 2(8 – 3)
Δp = 10kgms^-1 east

2. A 3kg cart has a velocity of 4ms^-1 east. It experiences a change in momentum of 15kg.m.s^-1 east. Calculate the new velocity.
Δp = m(v – u)
15 = 3 (v – 4)
v = 9ms^-1 east

Now be careful when an object changes direction!
3. A toy 3kg toy car is moving at 5ms^-1 east. It bounces off a wall at a velocity of 2ms^-1 west. Calculate the change in momentum.
(Be cautious : the velocity has changed direction!) Let us call the direction of the final velocity (west) Positive.
-----> (east)
&lt----- (west)
Δp = m(v – u)
Δp = 3( 2 – (-5))
Δp = 3(2 + 5)
Δp = 21kgms^-1 west
(the final answer sign is positive therefore we write west)

Change in Momentum is also called Impulse.
There is another way to calculate Change in Momentum (Impulse)
Δp = Ft
F is the Resultant Force
t is the time for which the force was acting.

4. A cart is traveling at a certain velocity when it experiences a force of 12N for 2 seconds. Calculate the change in momentum.
Δp = Ft
Δp = 12(2)
Δp = 24N.s
The Impulse is 24N.s

So . . . There are TWO methods to calculate Change in Momentum (Impulse)
Δp = m(v – u)
Δp = Ft
You use the method that works best with the example.

5. A 4kg cart is moving at 2ms^-1 rightwards. A force of 10N rightwards is now exerted on it for a certain period of time, and the new velocity becomes 8ms^-1.
5.1. Calculate the change in momentum
Δp = m(v – u)
Δp = 4(8 – 2)
Δp = 24kg.ms^-1
5.2.Determine for how long the force was exerted.
Δp = Ft
24 = 10t
t = 2,4 s