# Momentum Problem involving minimizing collision impact

1. Apr 22, 2014

### Dethrone

1. The problem statement, all variables and given/known data

I just did a lab on inelastic collisions and this was one of the discussion questions:

Consider a situation in which you are the driver of a car stopped at a red light and you see a car of similar mass approaching rapidly from behind. Use the results of your experiment to discuss possible strategies for reducing the impact of the impending collision. For example, should you take your foot off the brake? should you accelerate forward?

2. Relevant equations

M1v1i + M2vf1 = v (M1+M2)

3. The attempt at a solution

I equation above was the equation that the lab was based on. Initially, I thought this might have had to do with impulse, but time (I don't think) is a variable you can control in that situation. I've also thought of what would happen if you "accelerated forward", but it still doesn't make sense because that would just increase momentum, and a larger momentum doesn't really "reduce" the impact of a collision in anyway. A large momentum (at least to me) doesn't indicate the force/impact of a collision. Intuitively, I would imagine that accelerating forward would be the answer, but I don't know how to prove it, numerically.

2. Apr 22, 2014

### Wheelwalker

For an inelastic collision in which only one object is moving initially (let's call it object 1), the final velocity of the combined objects is given by $v_2=\frac{m_1}{m_1+m_2}v_1$. Now, the initial velocity $v_1$ is the velocity of the moving object but can also be thought of as the velocity of the moving object with respect to the reference frame of the stopped car (object 2). So, what would happen to the relative velocity of the vehicles if object 2 accelerated in the direction object 1 is traveling in?

3. Apr 22, 2014

### Dethrone

Wouldn't that decrease V1? Since the velocity of the first car is now relative to the moving second car, and not to a stationary car? Or am I just confused right now?

Also, if object 2 is moving too, wouldn't the formula above (v2= (m1/(m1+m2))vi) be invalid? Or would it not matter because we're talking about relative velocities? Maybe I'll just confused, haha.

4. Apr 22, 2014

### Wheelwalker

You're right, the equation above would be invalid for a reference frame at rest in which both cars have some initial velocity, which is what we should be considering. I'm just trying to give you a feel for how an equation like that might change when the car at rest starts accelerating. The relative velocities between the cars lowers and thus upon collision, the force is equal to the change in momentum over change in time. At a lower velocity, the second object should exert a smaller force on the car. You can also think about this problem in terms of kinetic energy and work. The moving car would have a higher kinetic energy to "spend" in the collision if it had a higher mass or velocity.

5. Apr 22, 2014

### Dethrone

Wow, I completely understand this now. Looking back, the solution to this problem (in my opinion) is quite ingenious. Thanks so much!

6. Apr 23, 2014

### Dethrone

I hope you're still here, because I have one more question! In the same inelastic collision experiment, how could you minimize the "momentum lost". For example, when I did the lab and calculated the initial and final momenta of the carts, I realized that the final momenta was always less than the initial. So I'm guessing that was "lost" due to external forces such as air resistance and friction.
My guess is that if the effect of air resistance on an object is negligible in comparison to the friction the cars experience, then the more I increase the velocity of the 1st car, the less momentum lost?