Kinetic energy dissipated during inelastic collsion

[jdawg]

Homework Statement

Blocks A and B are moving toward each other. Block A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of -25 m/s. They suffer a completely inelastic collision. The kinetic energy dissipated during the collision is:

Homework Equations

The Attempt at a Solution

So my professor has already worked out this problem, but I'm having trouble understanding why she picked the equations she did and how she manipulated them.

m₁v_1i-m₂v_2i=(m₁+m₂)V

Plug in the numbers and you get V=0

ΔK=$\frac{1}{2}$(m₁+m₂)V²-($\frac{1}{2}$m₁v_1i²+$\frac{1}{2}$m₂v_2i²)

Plug in and get -3750J

 

[rude man]

Almost.
There's no such thing as negative kinetic energy.
The problem did not ask for the CHANGE in k.e. It asked for the k.e. dissipated in the collision.

 

[jdawg]

Wouldn't the negative sign just mean that energy was lost? -3750 J was the answer my professor wrote down.

 

[rude man]

Wouldn't the negative sign just mean that energy was lost? -3750 J was the answer my professor wrote down.

No. Your instructor calculated the CHANGE in k.e. as indicated by the delta K:
" ΔK=1/2(m1+m2)V²-(1/2m1v1i²+12m2v2i²) ""

But the energy DISSIPATED is a positive number The word "dissipated" automatically implies a negative change in energy.

So this is just a semantic issue.

 

[jdawg]

No. Your instructor calculated the CHANGE in k.e. as indicated by the delta K:
" ΔK=1/2(m1+m2)V²-(1/2m1v1i²+12m2v2i²) ""

But the energy DISSIPATED is a positive number The word "dissipated" automatically implies a negative change in energy.

So this is just a semantic issue.

Ohh ok! Thanks, I think it makes sense now :)