Inellastic Collision Problem

[klopez]

The mass of the blue puck shown below is 30.0% greater than the mass of the green one. Before colliding, the pucks approach each other with momenta of equal magnitudes and opposite directions, and the green puck has an initial speed of 11.0 m/s. Find the speeds of the pucks after the collision if half the kinetic energy of the system becomes internal energy during the collision.

So...
green puck = m

blue puck = 1.30m


But I have no idea how to use conservation of energy and kinetic energy to solve this problem. Please help.

-Kevin

 

[Epimetheus]

First, introduce suitable variables. For example, let
$$p_b, p_g, m_b, m_g$$
be the momenta and masses of the two particles. You will need others. Your claim
"green puck = m; blue puck = 1.30m" is physically meaningless. What PROPERTY of the pucks are you assigning those values?

Can you compute the kinetic energy of the system before the collision? If not, would it help to compute another property of the system (the velocity of the other puck)? What statement in the problem allows you to find this quantity?

Can you determine the initial kinetic energy?

"Half of the kinetic energy of the system becomes internal energy ... " Now, can you find the final kinetic energy? What is the final momentum? Can you solve this system of two equations?

 

[Moetasim]

Hello Kevin,

Thank you for reaching out for help with this problem. I would approach this problem using the principles of conservation of momentum and energy.

First, let's define some variables and equations that we will use to solve this problem:

m1 = mass of green puck
m2 = mass of blue puck
v1 = velocity of green puck before collision
v2 = velocity of blue puck before collision
vf1 = velocity of green puck after collision
vf2 = velocity of blue puck after collision
KE1 = kinetic energy of green puck before collision
KE2 = kinetic energy of blue puck before collision
KEf1 = kinetic energy of green puck after collision
KEf2 = kinetic energy of blue puck after collision
Ei = initial total energy of the system
Ef = final total energy of the system

Now, we can use the principles of conservation of momentum and energy to solve for the final velocities of the pucks after the collision.

Conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum after the collision. In this case, we know that the initial momentum of the system is zero, since the pucks are approaching each other with equal and opposite momenta. Therefore, we can write the following equation:

m1v1 + m2v2 = m1vf1 + m2vf2

Next, we can use the given information to calculate the initial kinetic energy of the system:

Ei = KE1 + KE2 = (1/2)m1v1^2 + (1/2)m2v2^2

We also know that half of the kinetic energy of the system becomes internal energy during the collision. This means that the final kinetic energy of the system will be half of the initial kinetic energy:

Ef = (1/2)Ei

Now, we can write an equation for the final kinetic energy of the system using the final velocities:

Ef = (1/2)m1vf1^2 + (1/2)m2vf2^2

Since we know that half of the initial kinetic energy becomes internal energy, we can set these two equations equal to each other and solve for vf1 and vf2:

(1/2)Ei = (1/2)m1vf1^2 + (1/2)m2vf2^2

(1/2)m1v1^2 +