Solving Momentum & Energy Homework: Glider Collision

[twenty5]

Homework Statement

Two air track gliders of mass 0.30kg and 0.20 kg are moving towards each other with speeds of 0.50 m/s and 1.0m/s respectively. Take the direction of the more massive glider as positive.

A) if the collision is elastic, find the velocity of each glider after the collision.

Answer is: [ -0.70m/s , 0.80m/s ]

Homework Equations

m₁v₁ + m₂v₂ = (m₁ + m₂ ) v'

E_k = 1/2 mv²

for.. elastic equations i think..
E_k = E_k^'

The Attempt at a Solution

I've tried using the v₁^' and v₂^' equations and subbing in the values, but the answer was not correct O_O. Uhm.. I just need a little hand on where to go next! (Note: I've also tried drawing the diagrams and I think they are correct xP) okay I've got one of the answers.. -0.7m/s but with that 1 equation.. how do I get the other answer lol...

 

[Mattowander]

Your first two equations are not correct. How did you get those equations? Remember that in an eleastic collision, both momentum and energy are conserved.

 

[twenty5]

Your first two equations are not correct. How did you get those equations? Remember that in an eleastic collision, both momentum and energy are conserved.

1 quick question, how do I know if the system is a conserved momentum or... not? if it is conserved momentum.. I believe I would use 1/2 Mv^2 + 1/2 mv^2 = 1/2 mv'^2 + 1/2 mv'^2

(didn't put the little signs =P)

 

[Mattowander]

As I understand it, in nearly all collisions, momentum is conserved. In inelastic collisions, energy is not conserved.

 

[twenty5]

As I understand it, in nearly all collisions, momentum is conserved. In inelastic collisions, energy is not conserved.

mmm k that helped ^^

ok just want to double check here...

so basically.. for all or most questions that involve a collision other then inelastic, it's associated with the formula...

m₁v₁ + m₂v₂ = (m₁ + m₂ ) v'

EDIT: okay I just used that, and only got the final velocity of 1 of the objects lol...
errr.. still trying x.x
think i just got it ..

 

[twenty5]

blaghh nvm I didn't get the second final velocity..

 

[Mattowander]

No. That equation would be used for what are called perfectly inelastic collisions. In this situation, energy is NOT conserved, and the objects stick together. That's why the right hand side of the equation has the (m1+m2) term.

However, in this problem we are dealing with elastic collisions and so we would use this equation to represent the conservation of momentum.

m1v1 + m2v2 = m1V1f + m2V2f where the f subscript represents the velocity of the mass after the collision. Hopefully that helps!

 

[twenty5]

No. That equation would be used for what are called perfectly inelastic collisions. In this situation, energy is NOT conserved, and the objects stick together. That's why the right hand side of the equation has the (m1+m2) term.

However, in this problem we are dealing with elastic collisions and so we would use this equation to represent the conservation of momentum.

m1v1 + m2v2 = m1V1f + m2V2f where the f subscript represents the velocity of the mass after the collision. Hopefully that helps!

hm.. I think that cleans up some bit of stuff rofl thanks.. if I run into any trouble I'll post back in about 3 - 5 minutes

 

[twenty5]

If I use that equation.. wouldn't I have 2 unknown variables? V1f and V2f?

ok well, I used that equation and I ended up with

0.35 = 0.3v_1' + 0.2v₂'

 

[Mattowander]

You would. However, you can also use the fact that kinetic energy is conserved to formulate a second equation. With two equations and two unknown variables, you should be able to solve.

Remember, K.E. = 1/2mv^2

 

[twenty5]

uhmm I used the 1/2 mv₁² + 1/2mv₂² = 1/2 mv₁² + 1/2 mv₂²

... Ek1 + Ek2 = Ek1' + Ek2'...?

and I ended up with a weird number for V₁²'

 

[Mattowander]

What number did you end up with?

You need to use a combination of the conservation of energy equation and conservation of momentum equation. You have two unknown variables. You can solve for one of these unknown's in terms of the other unknown variable, and then plug that into the second equation

 

[twenty5]

What number did you end up with?

You need to use a combination of the conservation of energy equation and conservation of momentum equation. You have two unknown variables. You can solve for one of these unknown's in terms of the other unknown variable, and then plug that into the second equation

is the formula I typed right above your post correct?

 

[twenty5]

ok well I got Square Root of ( ( 0.1375 - 0.1v₂²')/ 0.15) = V₁'

 

[Mattowander]

uhmm I used the 1/2 mv₁² + 1/2mv₂² = 1/2 mv₁² + 1/2 mv₂²

... Ek1 + Ek2 = Ek1' + Ek2'...?

and I ended up with a weird number for V₁²'

The first equation is wrong ( or you forgot your subscripts ). You forgot to label the masses m1 and m2, and in your equation the velocities are the same on both sides. A more precise equation would be

1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1f^2 + 1/2m2v2f^2.

I know it's kind of confusing, especially typed out. Hopefully it makes sense to you!

 

[twenty5]

BUUMP still need help =/ I gots a test tomorrow