What Is the Loss of Mechanical Energy in a Car Collision?

[Iwanttolearn7]

Homework Statement

A 12000 kg car traveling at 10 m/s strikes and couples with a 6000 kg car at rest. What is the loss of mechanical energy in the collision?
Answer is 200,000 J.

Homework Equations

I want to know HOW to arrive at the correct answer above.

The Attempt at a Solution

Relevant equations tried:

1. Speed at final combination = Vf=(m1/m1+m2)Vi
=(12000/12000+6000)(10)
= 6.7 m/s

2. Kf-Ki
K= 1/2 mv^2
Kf= 1/2(12000)(6.7)^2 + 1/2(6000)(6.7)^2
= 269340 + 134670
= 404010
Ki= 1/2(12000)(10)^2 + 1/2 (6000)(10)^2
= 600,000 + 300,000
= 900,000

K=Kf-Ki
=404010 - 900,000
= -495990
=Not even close to the right answer.

I've done this problem over and over for two hours, not kidding, trying different combinations of equations, can someone please tell me where I am going wrong?

Thank you very much!
=

K

 

[turin]

It looks like you just messed up the initial kinetic energy calculation. How fast is the 6000 kg car travelling, initially?

 

[Iwanttolearn7]

Thank you for replying! The 6000 kg car is at rest.

 

[Iwanttolearn7]

So would that be:

Ki= 1/2(12000)(10)^2 + 1/2 (6000)(0)^2
= 600,000 + 0
= 600,000

Kf-Ki=
404010-600,000 = -195990, still incorrect. :(

 

[turin]

If you round 20/3=6.7 to only two sig. figs., then you should round -195990 to only two sig. figs., and then it is correct. However, what you should really do is keep 20/3, instead of brutally rounding it off at the beginning. Without rounding, it is correct exactly as given.

 

[Iwanttolearn7]

I apologize, I'm new to this. I don't understand what you mean by 20/3, which is not part of any of the equations. Should it be?

But you are so right about the rounding! Thank you! I was going crazy trying to figure it out:

Kf = 1/2(12000)(6.66666667)^2 + 1/2(6000)(6.66666667)^2
= 266666.7 + 133333.3
= 400,000

and the revised (thanks!)
Ki= 1/2(12000)(10)^2 + 1/2 (6000)(0)^2
= 600,000 + 0
= 600,000

So Kf-Ki =
400,000 - 600,000 = -200,000, negative because the energy is lost, correct?

Thank you ever so much, you have very much made my day!

 

[cepheid]

He meant, in the calculation of the speed after the collision:

(12000/18000)(10 m/s) = (dividing both numerator and denominator by 6000) = (2/3)(10 m/s)

= 20/3 m/s

This is the exact final velocity. Keeping this until the end will prevent the propagation of rounding errors. Try to simplify everything as much as possible before whipping out the calculator.

 

[Iwanttolearn7]

Ok, I get it, thank you very much!