[b]1. The problem statement, all variables and given/known data[/b]A 12000 kg ca

Question

[b]1. The problem statement, all variables and given/known data[/b]A 12000 kg car traveling at 10 m/s strikes and couples with a 6000kg car at rest. What is the loss of mechanical energy in thecollision? Answer is 200,000 J.

[b]2. Relevant equations[/b]

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

[b]3. The attempt at a solution[/b]

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 rightanswer.

I've done this problem over and over for two hours, not kidding,trying different combinations of equations, can someone please tellme where I am going wrong? Thank you very much!

Explanation / Answer

I found 2 errors: 1. I forgot that the initial velocity of the 6000 kg car is0. 2. Rounding the numbers too early caused a discrepancy in thefinal answer. Viola, solved! Kf = 1/2(12000)(6.66666667)^2 + 1/2(6000)(6.66666667)^2 = 266666.7 + 133333.3 = 400,000 and the revised 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 islost. Hey, I think people who find a way to solve their own problemsshould be able to be rewarded with points, extra points!

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