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Impulse-Momentum Theorem

Impulse rules my LIFE!!!
Added by MayWong

1 What is Impulse-Momentum Theorem
2 General info on Momentum
3 Other Ways to find Impulse
4 Origin of Impulse-Momentum Theorem
5 Relating to Newton's Second Law of Motion
6 Lets Review
- 6.1 Examples
  - 6.1.1 Stopping Cart Problem
  - 6.1.2 Car Collision Problem
- 6.2 Try it Yourself
7 Others' Work
8 Reference
- 8.1 Resources
- 8.2 Images

What is Impulse-Momentum TheoremEdit

The impulse-momentum theorem can be summarized and explained with the following equation:

J = delta p

General info on MomentumEdit

Momentum is P = mv! When an object has a mass and velocity, it has momentum. Since mass(m) is measured in kilogram[kg] and velocity(v) is measured in meters per second[m/s], momentum(P) is measured in kg*m/s. The mass and velocity are indirectly prkjsdftional to each other and directly proportional to the momentum.

Other Ways to find ImpulseEdit

The definition of Impulse is:

J = FΔt

J = Impulse, F = Force, t = time (Δt = change in time), and in French Je means me or I, (pronounced J) so if you think of I'm fat then you will remember this equation. Meaning you're fat, not me the writer, obviously.

By the impulse momentum theorem (and really it's using Newton's Second Law), we can find that:

J = mΔv

m = mass, v = velocity/speed (Δv= change in velocity/speed)

Origin of Impulse-Momentum TheoremEdit

There are no specific records as to who discovered the impulse-momentum theorem or when it was discovered. All we know is that it was derived from Newton's Second Law of Motion (F = ma). Other equations necessary to derived the impulse-momentum theorem are (a = Δv/Δt) and (P = mv)

Relating to Newton's Second Law of MotionEdit

Newton's Second Law of Motion: F = ma

Since acceleration (a) is equal to Δv/Δt you can replace the acceleration (a) in Newton's Second Law of Motion with Δv/Δt to get F = (mΔv)/Δt

To get rid of the fraction (or division), you can multiply both side with Δt and then the equation will become

FΔt = mΔv

mΔv = m(v2 - v1) = mv2 - mv1, and since {mv2 = P2} and {mv1 = P1}

then FΔt = mΔv = P2 - P1

we can now conclude that

                  J = FΔt, J = mΔv, or J = P2 - P1 !!!

F = Force, m = mass, a = acceleration v = velocity/speed P = momentum

Lets ReviewEdit

ExamplesEdit

Stopping Cart ProblemEdit

Question

A cart with a mass of 1.1 x 10^3 kg is moving with a speed of 1.7 x 10^2 m/s. The impulse required to bring the car to rest is?

Answer

J = ΔP = mΔv

m = 1.1 x 10^3 kg, v(i)= 1.7 x 10^2 m/s, v(f)= 0.0 m/s

J = 1.1 x 10^3 kg x (1.7 x 10^2 m/s - 0.0 m/s)

J = 1.87 x 10^5 N s

Car Collision ProblemEdit

Question

What is the impulse of car 'A' during the collision?

Answer

J = mΔv

You can see that the final picture on the right shows Car 'A' moving to the left when it was moving to the right in the beginning (refer to the 1st pic) at 4m/s. Since it changed direction, the final velocity/speed is actually -4m/s, while the initial velocity/speed is +8m/s.

m = 2000kg, v(i) = 8m/s, v(f) = -4m/s

J = mΔv = m(v(f)-v(i)) J = 2000[kg](-4[m/s]-8[m/s])

J = 2000[kg](-12[m/s])

J = -24000[N s]