Basic momentum/loss of energy question

[oreosama]

Homework Statement

Two skaters collide and grab onto each other on frictionless ice. one of them of mass "m₁" is moving to the right at "v₁", while the other, of mass "m₂", is moving to left at "v₂"

given m₁, m₂, v₁, v₂, determine:

the magnitude and direction of the velocity just after the collision
the loss in kinetic energy of the system

Homework Equations

p=mv

The Attempt at a Solution

m₁*v₁ - m₂*v₂ = (m₁+m₂)v₃

v₃ = (m₁*v₁-m₂*v₂) / (m₁+m₂)

firstly I should know if that was right.. then:

1/2*m₁*v₁^2 + 1/2*m₂*v₂^2 = 1/2(m₁+m₂)(v₃)^2

m₁*v₁^2 + m₂*v₂^2 = (m₁+m₂)(m₁*v₁-m₂*v₂)^2 /(m₁+m₂)^2

m₁*v₁^2 + m₂*v₂^2 = (m₁*v₁-m₂*v₂)^2 /(m₁+m₂)

(m₁*v₁^2 + m₂*v₂^2) (m₁+m₂) = (m₁*v₁-m₂*v₂) (m₁*v₁-m₂*v₂)

m₁^2*v₁^2 + m₁*m₂*v₁^2 + m₁*m₂*v₂^2 + m₂*v₂^2 = m₁^2*v₁^2 - 2*m₁*m₂*v₁*v₂ + m₂^2*v₂^2

m₁*m₂*v₁^2 + m₁*m₂*v₂^2 = -2*m₁*m₂*v₁*v₂
v₁^2 + v₂^2 = -2*m₁*m₂*v₁*v₂ / ( m₁*m₂)

2*v₁*v₂ + v₁^2 - v₂^2


there's a chance I have a clue I knew what I'm doing on the first part.. the second part clearly not?

 

[tiny-tim]

hi oreosama!

given m₁, m₂, v₁, v₂, determine:

the magnitude and direction of the velocity just after the collision
v₃ = (m₁*v₁-m₂*v₂) / (m₁+m₂)

firstly I should know if that was right..

yes

the loss in kinetic energy of the system
…
1/2*m₁*v₁^2 + 1/2*m₂*v₂^2 = 1/2(m₁+m₂)(v₃)^2

m₁*v₁^2 + m₂*v₂^2 = (m₁+m₂)(m₁*v₁-m₂*v₂)^2 /(m₁+m₂)^2

m₁*v₁^2 + m₂*v₂^2 = (m₁*v₁-m₂*v₂)^2 /(m₁+m₂)

the question asks for the difference in KE …

you should have a minus in the middle of those lines!

now just gather the v₁² terms, the v₂² terms, and the v₁v₂ terms​

 

[oreosama]

thanks for that

peddling along through this assignment I've come across:

A bomb of mass "m" at rest explodes. Half of the mass is thrown off in the +x-direction at a speed "v". A quarter of the mass is thrown off in the +y-direction at a speed "3v".

given[m,v]

determine the magnitude and direction of the remaining piece

determine the energy of the explosion

i have no idea what I'm supposed to do, but I would think everything should cancel out?

(1/2*m*v) i + (1/4*m*3v)i + something = 0

-(1/2*m*v) i - (3/4*m*v) j = something ?

everything begins at rest and blows up..

(1/2*1/2*m*v^2 + 1/2*1/4*m*(3v)^2) * 2 (the third piece being exact opposite of the first two means energy should be double the first 2 added up?)

...

11/4*m*v^2

 

[tiny-tim]

hi oreosama!

(just got up :zzz:)

A bomb of mass "m" at rest explodes. Half of the mass is thrown off in the +x-direction at a speed "v". A quarter of the mass is thrown off in the +y-direction at a speed "3v".

given[m,v]

determine the magnitude and direction of the remaining piece

determine the energy of the explosion

i have no idea what I'm supposed to do, but I would think everything should cancel out?

(1/2*m*v) i + (1/4*m*3v)i + something = 0

(try using the X² button just above the Reply box )

yes, momentum (and angular momentum) is conserved in every collision

but your equation should be (1/2*m*v) i + (1/4*m*3v)j + something = 0, shouldn't it?

try again ​