Conservation of energy

show that when Mass (m1) and kinetic energy (Q1) collide with a stationary particle (m2) it transfers an energy. Using conservation of energy and momentum

Q2 = (4M1M2)/(M1 + M2)^2 x Q1

Cheers

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- May 7th 2008, 10:56 AMj-lee00Conservation of energy
Conservation of energy

show that when Mass (m1) and kinetic energy (Q1) collide with a stationary particle (m2) it transfers an energy. Using conservation of energy and momentum

Q2 = (4M1M2)/(M1 + M2)^2 x Q1

Cheers - May 7th 2008, 11:48 AMtopsquark
I presume you simply mean find the kinetic energy of particle m2 after the collision.

where is the velocity of m1 before the collision and are the final velocities.

Solve the momentum equation for and plug it into the energy equation. After a few steps:

Solve this for . Hint: Use the quadratic formula.

So use this to find and find .

-Dan - May 7th 2008, 12:38 PMDanshader
Hello there,

you need to consider fractional lost in kinetic energy to obtain that equation:

fractional lost in Kinetic Energy

= (lost in Kinetic Energy)/(initial Kinetic Energy) → (1)

given for mass 1:

mass =

velocity before collision =

velocity after collision =

for mass 2:

mass =

velocity before collision =

velocity after collision =

using principle of conservation of momentum:

from velocity of approach = velocity of separation

or

Substituting into (2):

From equation (1):

= (lost in Kinetic Energy)/(initial Kinetic Energy)

lost in kinetic energy is gained by the stationary mass hence we can rewrite the equation as:

kinetic energy of mass m2/ initial kinetic energy

therefore;

kinetic energy of mass m2 = (initial kinetic energy)

Q2 = Q1

There is another way to get the answer but i think this should be sufficient unless you really want to know more xD cheers!