Energy Loss in Head on Collision of Two Cars w/Same Speed and Mass

[mrsteve]

Homework Statement

Two railroad cars, each with a mass of 7,000kg and traveling at 90 km/h collide head on and come to rest. How much mechanical energy is lost in this collision?

Homework Equations

KE=\frac{1}{2}mv^2

The Attempt at a Solution

KE=\frac{1}{2}(7000)(90)^2=2.835*10^7

Mechanical energy = KE+PE. PE = 0.

Energy lost = 2KE or 5.67*10^7

Book answer is 4*10^6

Where am I going wrong? Thanks..

 

[lewando]

If your result is in joules, the velocity units of km/h is not helping.

 

[Doc Al]

Convert the speed to standard units of m/s.

 

[mrsteve]

Ahh... So 90 km/h = 25 m/s.

\frac{1}{2}(7000)(25)^2=2.1875*10^6 => 2.1875*10^6(2) = 4.375*10^6 => 4*10^6

Thanks!