What Mass Ratio Causes Combined Mass to Move with Lesser Energy Mass?

[devanlevin]

2 balls, with masses of M1, M2, are involved in a plastic collision, one dimentional.. the kinetic energy of the ball m1 is 20 times that of m2. at what ratio between the masses will the new mass(m1+m2) move in the direction the lesser energy mass mas moving.

it seems to me that there is too much missing information here, but what i think i need to do is find the ratio between the masses that eventhough the 1st mass has more kinetic energy, the 2nd mass has more momentum. not sure how to do this,

but i think i need to find it through the fact that the energy grows like V^2 but the momentum like V,

so i need a case where P2>P1 but Ek1>Ek2, so M1<M2 but V1>V2,

the difference between M2,M1 should be greater than the difference between V1, V2 so that the momentum of M2 is greater, but the energy of M1 is still greater.

is this right? how do i find this?

also it is not said in which direction they are moving, if they are moving in the same direction, it is obvious that after the collision they will move in the direction of M2, which is also the direction of M1

there are three answers
m2/m1>0.05 when (m1)--> [m2]->

m2/m1>20 when (m1)--> <-[m2]

m2/m1<0.05 when [m2]-> (m1)-->

the 3rd case disproves what i said, ie V1>V2, but i think it is only because they are moving in the same direction.

 

[anathema]

you are correct in stating that there is not enough information given to accurately determine the ratio between the masses. Without knowing the initial velocities and directions of the two balls, it is impossible to calculate the ratio between their masses in order for the combined mass to move in the direction of the lesser energy mass.

In order to accurately determine this ratio, we would need to know the initial velocities and directions of the two balls before the collision, as well as the coefficient of restitution (a measure of how much energy is lost during the collision). With this information, we could use the conservation of momentum and the conservation of energy equations to solve for the ratio between the masses.

Additionally, the statement that the energy grows like V^2 and the momentum like V is not entirely accurate. The kinetic energy is equal to 1/2 * mass * velocity^2, while momentum is equal to mass * velocity. So, while the velocity does play a role in both equations, the relationship is not a direct proportionality.

In summary, without more information, it is not possible to accurately determine the ratio between the masses in order for the combined mass to move in the direction of the lesser energy mass.

 

[thomate1]

I would agree that there is not enough information provided to accurately determine the ratio between the masses in this scenario. However, your approach in considering the relationship between momentum and kinetic energy is correct. In a plastic collision, the total momentum of the system is conserved, but the total kinetic energy may not be. This means that the resulting velocities of the masses after the collision will depend on the ratio of their masses.

To find the ratio between the masses, we can use the conservation of momentum equation:

M1V1 + M2V2 = (M1 + M2)V'

where V' is the resulting velocity of the combined mass (M1 + M2).

Since we know that the kinetic energy of M1 is 20 times that of M2, we can also use the equation for kinetic energy:

Ek1 = 1/2M1V1^2 = 20 x 1/2M2V2^2 = 10M2V2^2

We can rearrange the first equation to solve for V' and substitute it into the second equation to eliminate V'.

V' = (M1V1 + M2V2) / (M1 + M2)

Ek1 = 10M2V2^2 = 10M2((M1V1 + M2V2) / (M1 + M2))^2

Solving for M2/M1, we get:

M2/M1 = (10V2^2 - V1^2) / (V1^2 - 10V2^2)

This equation can be used to determine the ratio between the masses in each of the three cases you mentioned. However, as you pointed out, the direction of the velocities is also important in determining the resulting velocities after the collision. Without this information, it is not possible to accurately determine the ratio between the masses.