# Impulse-Momentum Theorem

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**What is Impulse-Momentum Theorem**Edit

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

J = delta p

**General info on Momentum**Edit

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 proportional to each other and directly proportional to the momentum.

**Other Ways to find Impulse**Edit

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: Yes

J = mΔv

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

speed)

**Origin of Impulse-Momentum Theorem**Edit

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 Motion**Edit

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 Review**Edit

### 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 (0.0 m/s - 1.7 x 10^2 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]

### Try it YourselfEdit

1. The magnitude of an object's momentum is 23kg*m/s. If the velocity of that object is doubled, the new momentum of the object is?

2. A mother pushed a child on a swing by exerting 15N force over a time of .3s. What impulse is delivered to the child?

3. An impulse of J is applied to an object. The change in the momentum of the object is?

- J
- 2J
- J/2
- 4J

4. Momentum may be expressed in

- joules
- watts
- kilogram * meters per seconds-sq
- Newton-seconds

## Others' WorkEdit

The following links were all created by other students from LAB. They all have information related to impulse of momentum.

1. http://schools.wikia.com/wiki/Momentum

2. http://schools.wikia.com/wiki/Momentum:_Collisions

3. http://schools.wikia.com/wiki/Momentum_Conservation:_Explosions

**Reference**Edit

### ResourcesEdit

1. Zitzewits, Paul W. Glencoe PHYSICS Principles and Problems (1999)

2. Lazar, Miriam A. and Tarendashm, Albert S. Barron's Review Course Series Let's Review: Physics

3. Wong, May. Physics Binder 2005-2006. :D

### ImagesEdit

http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1b.html (football)

http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1c.html (baseball)

http://physics.k12albemarle.org/impulse/Quiz/testc.htm (Car Collision Problem)

http://www.bible.ca/marriage/parenting.htm (Baby Swinging)