Momentum and Impulse

Why would it be hurt for you if you were hit by a stone instead of a chocolate bar, when they are both moving at a same speed? Why would you feel painful if you were hit by a flying bullet, instead of a stationary one?

This has something to do with the physics term—momentum, which is the quantity of movement of a moving object, measured as its mass(kg) multiplied by its velocity(m/s). Therefore, the unit of momentum is kg*m/s( or N*s). Also, momentum is a vector          ( involving both magnitude and direction) because velocity is vector.

When either the mass or the velocity of a certain object changes, its momentum would change. The change in momentum has another name—impulse. Generally, there are two scenarios for that. One is that the velocity of the object changes, but its mass stays the same, another is that the mass of the object changes whereas its velocity stays the same. This can be described as:

Δp = pf - pi ,

Δp = mVf - Vi ,

Δp = m(Vf - Vi) ,

Δp = mΔV

or

Δp = pf - pi ,

Δp = Vmf - Vmi ,

Δp = V(mf - mi) ,

Δp = VΔm

If you are not a physicist, then try not to consider the scenario where the mass and velocity of a certain object change simultaneously.

I am going to give you an example in order to help you understand.

Example: Joker increased the velocity of his 500-kg Lamborghini from 20/s to 80m/s. What is its change in momentum, or impulse?

The answer is: Δp = mΔV = (500kg)(80m/s - 20m/s)= 30000kg*m/s.

(Tips: Don’t try to stop Joker unless you are the Batman!)

Do you think we can only do calculations involving momentum and impulse with this formula? Absolutely not. Remember the formula Fnet = ma based on Newton’s Second Law? That is where our second formula involving momentum and impulse comes from:

Fnet = ma,

m = Fnet /a,

m = Fnet /(ΔV/ t)

Δp = Fnet /(ΔV/ t)*ΔV

Δp = Fnet*t

Using this formula, we shall be also be able to answer the questions at the beginning of this paper. According to Newton’s Third Law (when one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body), two colliding objects experience equal and opposite forces for the same amount of time. Therefore, their impulses must be equal and opposite. In other words, when you are hit by an object, you are experiencing the exact same impulse as the object does. Although the stone and chocolate bar were moving at the same speed, their mass were different. A stone was much heavier than a chocolate bar. Therefore, a stone could bring a bigger impulse. Whether or not you would feel hurt was determined by how much impulse you were experiencing. Similarly, although a flying bullet had the exact mass as the stationary one, the flying bullet was moving way quickly. Therefore, the impulse it brought was much bigger, which means more hurt to you.

Using this formula, we shall also be able to explain why the airbag in a car is so useful. When a car collides something, both the car’s mass and velocity stay the same. The only thing we can change is the time of collision. According to the formula, the bigger t is, the smaller Fnet will be. That is to say, airbags ensure drivers’ safety by prolonging the time of collusion when an accident occurs. I will give you an example to let you see the importance of having a airbag in your car.

Example: Joker paid the penalty for driving extremely fast. Fortunately, Joker was still alive because the airbag in his Lamborghini. The airbag prolonged the collision for one second. Without the airbag, Joker would collide the wheel of his Lamborghini within 0.005s. Calculate the force that Joker felt.

Answer: Fnet*t = mΔV, Fnet = mΔV/t = (500kg)(0m/s - 80m/s)/ 0.005s+1s = -39801N

Now let’s see, what would happen to Joker if there wasn’t an airbag in his Lamborghini?

The force that Joker experienced would be

Fnet = mΔV/t= (500kg)(0m/s - 80m)/ 0.005s =-8000000N

See? Although the airbag prolonged the time of collision for only one second, its effect was enormous!

You may want to ask, what kinds of people invented the marvelous airbag? The answer is Safety Engineers. They put theory into practice. Actually, designing airbags for cars is not the only responsibility for Safety Engineers. Generally, they are responsible for safety-critical diagnostic requirements and controls design for electric machine and power electronics system. They will lead safety-critical requirement development for electric drive and support vehicle-level safety critical requirement development.

In general, if you want to be a Safety Engineer, you have to major electric motor controls or power electronics, occupational health/safety, environmental health, engineering and the physical sciencein university. It is not an easy job!

According to the statics, the average income of Safety Engineers is $70,310 per year. Are you interested in that?