# Energy Conservation of a car collision

#### BMWPower06

1. Homework Statement
A car moving with an initial speed v collides with a second lighter stationary car that is 58.3% as massive. After the collision, the two cars stick together and move off in the same direction as before. Calculate the final speed of the two cars after the collision. Give your answer in units of the initial speed (i.e. as a fraction of v).

2. Homework Equations
M1V1+M2V2=M1Vf1+M2Vf2

3. The Attempt at a Solution
M1V1=M1Vf+53.8%M1Vf

I ended up with V/.538=Vf but it says im wrong, any1 know what im doing wrong?

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#### CaptainZappo

The final answer you have reported says the final velocity is greater than the initial velocity. Intuitively, you should know this is wrong.

You have M1V1=M1Vf+53.8%M1Vf

This setup is correct, so I think your error lies in your algebra. Try reworking the simple cleanup steps and see what happens.

PS: Your title is misleading, because your question is more concerned with the conservation of momentum, rather than the conservation of energy.

1. Homework Statement
A car moving with an initial speed v collides with a second lighter stationary car that is 58.3% as massive. After the collision, the two cars stick together and move off in the same direction as before. Calculate the final speed of the two cars after the collision. Give your answer in units of the initial speed (i.e. as a fraction of v).

2. Homework Equations
M1V1+M2V2=M1Vf1+M2Vf2

3. The Attempt at a Solution
M1V1=M1Vf+53.8%M1Vf

I ended up with V/.538=Vf but it says im wrong, any1 know what im doing wrong?

Last edited:

#### BMWPower06

The final answer you have reported says the final velocity is greater than the initial velocity. Intuitively, you should know this is wrong.

You have M1V1=M1Vf+58.3%M1Vf

This setup is correct, so I think your error lies in your algebra. Try reworking the simple cleanup steps and see what happens.

PS: Your title is misleading, because your question is more concerned with the conservation of momentum, rather than the conservation of energy.
k, so i got V/1.583=Vf

is that right? i plugged it in online but it says its wrong...

#### CaptainZappo

k, so i got V/1.583=Vf

is that right? i plugged it in online but it says its wrong...
That is the answer I came up with.

Perhaps someone else can chime in?

#### Ks. Jan Jenkins

mv = (m + .583m)v'
v/v' = 1.583
or

v'/v = .631(7)

The question asks for Give your answer in units of the initial speed (i.e. as a fraction of v), so you want v'/v not v/v'. In significant units it is .632.

#### Ks. Jan Jenkins

Oh, and I thought I would mention that your problem doesn't actually concern Energy Conservation, but rather the conservation of momentum. Kinetic Energy is usually not conserved in non-elastic collisions.

JJ +