Basic momentum/loss of energy question

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Homework Help Overview

The discussion revolves around two separate problems involving momentum and energy conservation in collisions and explosions. The first problem involves two skaters colliding on frictionless ice, while the second problem concerns a bomb explosion resulting in multiple fragments being propelled in different directions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the conservation of momentum and kinetic energy in the context of collisions and explosions. The original poster attempts to derive the post-collision velocity and kinetic energy loss for the skaters, while others question the correctness of their equations and suggest adjustments. In the explosion scenario, participants discuss the conservation of momentum and the implications of mass distribution and direction of motion.

Discussion Status

Some participants have provided affirmations regarding the correctness of initial momentum calculations, while others have pointed out potential errors in the kinetic energy calculations. The discussion is ongoing, with multiple interpretations being explored regarding the explosion problem and the conservation principles involved.

Contextual Notes

Participants express uncertainty about the setup and calculations, particularly in the second problem where assumptions about momentum cancellation are questioned. There is a focus on ensuring the correct application of 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


there's 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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