Inelastic Collision and Conversation of Momentum Question

[Shark 774]

Ok guys, so I know I post a lot of questions but I really need to get this straightened out! Haha.
So here's a situation I thought of, and I can't find out what's wrong with my theory... Help would be greatly appreciated.

A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of 25m/s to the left, before the collision. 30% of the total kinetic energy, before the collision, is transferred into heat/sound, etc. If the car and truck stick together after the collision and continue moving together, find the velocity that they move with.
(Assume no air resistance, blah, blah, blah).

∑Eki = 0.5 x 500 x (30)^2 + 0.5 x 1500 x (25)^2 = 693,750J
∑Ekf = (70/100) x ∑Eki = 485,625J
∑Ekf = 0.5 x (500+1500) x v^2
Therefore, v = Sqrt[(485,625x2)/2000] = 22m/s (to the left)
However from this we can get:
initial momentum = 500 x 30 + 1500 x -25 = -22,500kg m/s (treating right as the positive direction)
final momentum = (1500 + 500) x -22 = -44,000kg m/s
Therefore final momentum > initial momentum, which clearly can't be right!! What's wrong with my theory/calculations??

Thanks guys.

[Shark 774]

Maybe I can't simply use the change in kinetic energy to calculate the momentum, but instead I have to use the conversation of momentum and then from that I could work out the change in kinetic energy?

[/0]

maybe they arewrong about the energy lost because if u think about it u can solve the problem with just momentum yep and momentum is always conserved that's a truth my friend

[Shark 774]

Yeah thanks. I created the question myself, so that explains why it doesn't all add up haha.

[/0]

With inelastic collisions, if you have both initial speeds, you really only need conservation of momentum to solve for the final speed.

However, with collisions where they don't stick together, if you're given initial speeds but none of the final speeds then you need both conservation of moment and conservation of energy.

The above type of question you posed might work in the following ways:

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of 25m/s to the left, before the collision. 30% of the total kinetic energy, before the collision, is transferred into heat/sound, etc. If the car and truck don't stick together after the collision and continue moving together, find the final velocities of each vehicle."

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of u m/s to the left, before the collision. 30% of the total kinetic energy, before the collision, is transferred into heat/sound, etc. If the car and truck stick together after the collision and continue moving together, find the velocity v that they move with, and the initial velocity of the truck, u."

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of 25m/s to the left, before the collision. If the car and truck stick together after the collision and continue moving together, find the velocity that they move with, and find the energy kinetic energy lost."

[Shark 774]

With inelastic collisions, if you have both initial speeds, you really only need conservation of momentum to solve for the final speed.

However, with collisions where they don't stick together, if you're given initial speeds but none of the final speeds then you need both conservation of moment and conservation of energy.

The above type of question you posed might work in the following ways:

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of 25m/s to the left, before the collision. 30% of the total kinetic energy, before the collision, is transferred into heat/sound, etc. If the car and truck don't stick together after the collision and continue moving together, find the final velocities of each vehicle."

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of u m/s to the left, before the collision. 30% of the total kinetic energy, before the collision, is transferred into heat/sound, etc. If the car and truck stick together after the collision and continue moving together, find the velocity v that they move with, and the initial velocity of the truck, u."

"A car with a mass of 500kg collides with a truck of mass of 1500kg. The car has a velocity of 30m/s to the right, before the collision. The truck has a velocity of 25m/s to the left, before the collision. If the car and truck stick together after the collision and continue moving together, find the velocity that they move with, and find the energy kinetic energy lost."

Great response, thanks a lot!

[Shark 774]

Don't know if you checked the answers for those examples that you gave, but I got:
1: Car final velocity = 44.07m/s left, truck final velocity = 0.3098m/s left.
2: Initial velocity of truck = 308.7m/s left, final velocity together = 224.1m/s left.
3: Final velocity together = 11.25m/s left, Ek lost = 81.76%

Cheers -

[/0]

i think it's pretty much correct :]
well done

But did you get multiple solutions for Q1 and Q2? Q2 seems to have two physically valid solutions, whereas Q1 only has one, the one you gave.

The other solution for Q2 is:
Initial velocity of truck = 8.7m/s right, Final velocity together = 14.1 m/s right.
This seems to be another physically possible scenario.

(The other solution for Q1 is:
Final velocity of car: 21.6 m/s right, Final velocity of truck: 22.2m/s left. One of the assumptions we have to make is that they can't pass through each other :p)

[Shark 774]

Yeah, I did get two solutions, but for the second question you said that the truck is moving LEFT initially. And for the first one, yeah, we assume they can't pass through each other haha but also you said they continue in the same direction. Thanks a lot for your help and examples, cleared this up a lot for me!

[/0]

Lol my bad then , gj