# Car Collistion using conservation of momentum

## Homework Statement

Two Cars
Yellow: Moving South
Green: Moving West

Green car stop in center of intersection and gets hit on from south bound Yellow Car

They collide, at intersection, find initial velocity, impact velocity and momentum (this confuses me)

Yellow Mass - 1356 kg
Green Mass - 829 kg

Skid Marks
North-South - 13.18m
East-West - 11.2m
Curved Skid - 3.442 (don't know how relevant)
Yellow front tire is 18.35m from southern end of north-south skids marks (again, not sure how relevant)

Kinetic Friction - 0.8

According to tutor, not able to use energy or time at all. Conservation of momentum should be enough.

I THINK the collision is inelastic and total momentum is conserved.

## Homework Equations

$v^2 = u^2 + 2as$

$m_1v_1 + m_2v_2 = m_1v_1 + m_2v_2$

## The Attempt at a Solution

I believe I was able to figure out the initial velocities, but don't know how to proceed or even if I am correct.

Friction Force = (-0.8) * (9.81) = -7.84 m/s^2

Yellow
$u^2 = v^2 + 2as$
$u^2 = 0 + 2 * -7.84 * 13.18$
$u^2 = -206.66$
$u = \sqrt{266.66}$
$u = 14.37 m/s$

Same for Green car to get 13.25 m/s

Please help if you are able, the first set of answers (using time and energy) were not accepted as I didn't know you couldn't use them.

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CWatters
Homework Helper
Gold Member
I agree with your calculation for the green car but not the yellow.

The green car is stationary when hit so the 11.2m east west skid mark can be used to work out it's initial velocity.

The friction force = 0.8 * mass * g

F = m * a

a = F/m = 0.8 * g

V2=U2 + 2as

U2 = - 2as

U = SQRT (2 * 0.8 * g * 11.2)

= 13.25m/s (eg same as you got).

However the yellow car undergoes a three part process..

1) The initial skid reduces the velocity but does not stop the car.
2) An impact
3) A second skid to a stop.

I believe you have to work the problem backwards. Taking part 3 first.. You can work out how fast the yellow car was going after the impact from the length of the second skid.

You then need to apply conservation of momentum to work out how fast the yellow car was going before the impact. To do that I believe you also need to work out the velocity of the green car after the impact from it's second curved skid.

At this point you will have the velocity and mass of both cars after the impact so you can sum the momentum after the impact.

You know the momentum of the green gar before impact (=0) so easy to work out the momentum of the yellow car at impact.

Then calculate the velocity of the yellow car at impact.

Finally the velocity of the yellow car at the start of the initial skid.

CWatters
Homework Helper
Gold Member
Just to clarify..

I believe this bit of your calculation...
Yellow
$u^2 = v^2 + 2as$
$u^2 = 0 + 2 * -7.84 * 13.18$
$u^2 = -206.66$
$u = \sqrt{266.66}$
$u = 14.37 m/s$
is wrong because the yellow car does not stop at the end of it's first skid so V2 is not zero. I believe you need to calculate V from what happens after the impact.

Ok, I will do those calculation in the morning.

So I'm 100% on this, the process is.
1. Find Velocity of Yellow after impact
2. Then impact velocity
3. Initial velocity of yellow
4. Then apply conservation of momentum steps

Also, am I able to get 1-3 from the previously used equation or what I have to use something else

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CWatters
Homework Helper
Gold Member
No.

1. Find Velocity of Yellow car after impact
2. Find Velocity of green car after impact
3. Apply conservation of momentum to calculate Velocity of yellow car at impact (green car is stationary).
4. Calculate Velocity of yellow car at start of first skid.

1. and 2. come from V2=U2+2as. For both cars V2=0 and you need to calculate U.

4. also comes from V2=U2+2as. In this case V comes from step 3 and you need to calculate U.

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