Impulse Force Model Review

Impulse-Momentum Force Model

The Impulse-Momentum theorem is Fnet(change in t) = change in(mv). This formula can be used to calculate the momentum of an object in certain situations.

For example, if a 1000kg sports car is traveling at 30.0 m/s, you can plug those numbers into the equation to solve for the momentum.

P represents momentum. The equation can be represented as P = mv. So, if m = 1000km and v = 30.0 m/s, multiplying them will give you the P - value: 30,000 kg. 

Impulse is also relevant in this model. Impulse = Change in Momentum. (Change in P = J). 

Impulse is represented as J. So, the formula we can use is Change in P = m(change in v).

So, if we return to the sports car scenario, we can calculate the impulse needed to increase the car's speed from 30.0 m/s to 35.0 m/s.

Change in P = m(change in v)

Change in P = (1000)(v final - v initial)

Change in P = (1000)(34 - 30)

Change in P = 5,000 kg

Using a new formula, J = F(change in t), we can determine the forces acting upon the sports car in the scenario. If the car were to crash, we could find the amount of force the object the car crashes into exerts on the car.

If the car, traveling 35 m/s, crashes into a rock wall and comes to rest at 0.25 seconds, we can plug the numbers into the equation to find the force exerted on the car by the wall.

* The force becomes negative depending on which direction it is exerted In this situation, the J will be negative because the car's force on the wall is positive. So, the wall's force back on the car will be negative.

J = F(change in t)

J = Change in P = mv = 100(35) = 35000

- 35,000 = F(0.25)

- 35,000/.25 = F/.25

- 140,000 N = F

Newton's 2nd Law is also applied in this scenario. A common misconception is that the wall would exert more force on the car because it is bigger. However, according to N2L, the forces are the same. Because the wall has a greater mass, the effect of the crash will be greater on the car. 

Diagrams can also be used to help visualize Impulse Force Model scenarios. 

For example, if the scenarios is that of a car and truck crash, we can examine the situation and create a momentum conservation diagram. If the truck is 5000 kg and rear-ends the 1200 kg car that had been traveling at 13 m/s, the truck would be slowed from 14 m/s to 12 m/s and the car would speed up.

Initial object/mass/velocity:

Final object/mass/velocity:

The momentum conservation equation would be mava + mbvb = mava + mbvb. Because we are comparing the initial event with the final event, we set them equal to each other.

mava + mbvb = mava + mbvb

(500)(14) + (1200)(13) = (500)(12) + (1200)(v)

70,000 + 15,600 = 60,000 +1200v

85,600 = 60,000 + 1200v

25,600 = 1200v

v = 21.3 m/s

When the momentum is larger, the change in velocity will be smaller and, when the momentum is smaller, the change in velocity will be larger.

M(change in v) = m(CHANGE IN V)

When comparing the truck and the car, we can determine that the change in momentum and the force of impact are equal because of N2L: 

"The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object."

F = Ma and F = mA

The acceleration can be found using the formula a = Fnet/m.