Collision problem in momentum

1. Nov 8, 2012

Violagirl

1. The problem statement, all variables and given/known data
A car moving to the right at 40 m/s has a mass of 2000 kg. It strikes a car of mass 1500
kg and both cars immediately come to rest. What was the speed and direction of the
second car just prior to the collision?

2. Relevant equations

pinitial=pfinal

p=mv

K=1/2mv2

3. The attempt at a solution

In determining the speed of the second car, I set up my formula to try to resemble what the problem provides in how the first car is moving:

If pinitial=pfinal, then:

m1v1=m2v2

I set it up like this since we're only told that the first car is traveling in a given direction towards the second car and we we want it so that we can find v2. So:

(2000 g) (40 m/s) = (1500 g)v2

v2=53.3 m/s

Otherwise, I'm not sure what approach to take the find the direction. I thought maybe in the x direction with sin equaling 180 degrees with car one in applying the kinetic energy equation but I am not exactly sure if this is correct.

2. Nov 8, 2012

Simon Bridge

What does that imply about the direction of the second car?
If "to the right" (the direction of the 1st car) is the +x direction, then 180 degrees from the +x direction is what?

You could try doing it formally - call the direction of the first car +x and write out vector equations:

before collision:
$\vec{p}_{b}=p_1\hat{\imath}+\vec{p}_{2}=(m_1v_1+m_2v_2\cos{\theta})\hat{\imath}+m_2v_2\sin(\theta)\hat{\jmath}$

after collision:
$\vec{p}_{a}=0$

conservation of momentum:
$\vec{p}_a = \vec{p}_b$

... gives you two equations and two unknowns.

If $\theta=0$ then car-2 is travelling in the same direction as car-1; which is to say: "to the right".
To get full marks, you should always try to provide final answers using the same terms as used in the question.

In general: if you lay out all conservation-of-stuff problems like this, you'll find them easier to think your way through.

Note: write the expression for total kinetic energy before and after the collisions.
Is there any value for $v_2$ (your only unknown) which will make KE before equal KE after? i.e. is kinetic energy conserved in the collision?

Last edited: Nov 8, 2012
3. Nov 9, 2012

Basic_Physics

Both cars are moving initially and "finally" both are stationary.
So pinitial need to have both components and pfinal = ....