- #1
Tibriel
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Conservation of Momentum vs. Energy in "sticking" collisions
So here's the deal I'm wondering why when you have a collision where the two objects stick together momentum is conserved but energy isn't. (or at least that's how I'm reading what my math is telling me)
Example problem: 2 cars going into a head-on collision that stick together upon contact
Car 1:
m = 10kg
v = 5m/s
Car 2
m = 10kg
v = -10m/s
What is the velocity after the collision assuming no energy is lost to Friction/sound/heat etc.
p(before) = mv[car 1] + mv[car 2] = p(after) = (m + m)v [car 1&2 combined]
KE = (1/2)*mv^2
well I get a p(total) = -50kgm/s
and a v(combined) = -2.5m/s
I get an inital KE of 375J (500J - 125J) and a final KE of 62.5J if I use the new velocity from the momentum equations
So why is energy decreased when they stick together?
My assumption is that the KE of each car gets decreased because they are doing work on each other. This explanation sounds incomplete to me. I'm thinking that the rest of the explanation involves the change in velocity for each car. Here both have a change of 7.5m/s
Any help would be greatly appreciated
Homework Statement
So here's the deal I'm wondering why when you have a collision where the two objects stick together momentum is conserved but energy isn't. (or at least that's how I'm reading what my math is telling me)
Example problem: 2 cars going into a head-on collision that stick together upon contact
Car 1:
m = 10kg
v = 5m/s
Car 2
m = 10kg
v = -10m/s
What is the velocity after the collision assuming no energy is lost to Friction/sound/heat etc.
Homework Equations
p(before) = mv[car 1] + mv[car 2] = p(after) = (m + m)v [car 1&2 combined]
KE = (1/2)*mv^2
The Attempt at a Solution
well I get a p(total) = -50kgm/s
and a v(combined) = -2.5m/s
I get an inital KE of 375J (500J - 125J) and a final KE of 62.5J if I use the new velocity from the momentum equations
So why is energy decreased when they stick together?
My assumption is that the KE of each car gets decreased because they are doing work on each other. This explanation sounds incomplete to me. I'm thinking that the rest of the explanation involves the change in velocity for each car. Here both have a change of 7.5m/s
Any help would be greatly appreciated