Basic momentum/loss of energy question

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The discussion revolves around two skaters colliding on frictionless ice, where one skater has mass "m1" and velocity "v1" to the right, while the other has mass "m2" and velocity "v2" to the left. The post-collision velocity "v3" is calculated using the formula v3 = (m1*v1 - m2*v2) / (m1 + m2). The participants also explore the loss of kinetic energy, emphasizing the need for a correct equation to find the difference in kinetic energy before and after the collision. Additionally, a related problem about a bomb explosion is introduced, focusing on momentum conservation and the calculation of the remaining mass's velocity and explosion energy. The conversation highlights the importance of correctly applying conservation laws in both scenarios.
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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


theres a chance I have a clue I knew what I'm doing on the first part.. the second part clearly not?
 
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hi oreosama! :smile:
oreosama said:
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 :smile:
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! :rolleyes:

now just gather the v12 terms, the v22 terms, and the v1v2 terms​
 
thanks for that :bugeye:

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
 
hi oreosama! :smile:

(just got up :zzz:)
oreosama said:
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 :wink:)

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? :wink:

try again :smile:​
 

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