Double Ball Drop: Solve Elastic Collision Velocity Problem

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In summary, the conversation discusses the problem of calculating the velocity of two balls after an elastic collision with the ground. The equations used are the conservation of energy and linear momentum. The solution involves solving a quadratic equation with two unknowns.
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Gibanga
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Homework Statement



Hi everyone. Hope I'm not breaking any forum rules, because I've alread wrote this one in another thread by mistake. Here is where it should be.

Two balls of different mass are dropped one in top of the other, with the light one on top. After they collide with the floor (elastic collision), what is the velocity of both balls?

m is the mass of the small ball
M is the mass of the heavier one
v is the velocity of both balls before the collision with the ground
v1 and v2 are the velocities of the lighter and heavier ball respectively.

Homework Equations



pi=pf

The Attempt at a Solution



(m + M)v = mv1 + Mv2

What do i assume now?

I first assumed that mv1 = -(m+M)v + Mv2
but it doesn't look right to me because v1 turns out 2v2.

What am i doing wrong?

Thanks in advance.
 
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  • #3


tiny-tim said:
Hi Gibanga! Welcome to PF! :smile:


Hint: https://www.physicsforums.com/library.php?do=view_item&itemid=38" means that energy is conserved. :wink:

Thank you very much.

Linear momentum is also conserved.

So i get two equations and two unknowns and a very ugly quadratic equation jumps out of there. Should i solve it or am i wasting my time? This looks like a very simple problem and I'm just making it more complex...
 
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FAQ: Double Ball Drop: Solve Elastic Collision Velocity Problem

What is the Double Ball Drop experiment?

The Double Ball Drop experiment is a physics experiment that involves two balls of different masses being dropped from a certain height and colliding with each other. This experiment helps to demonstrate the principles of elastic collisions and conservation of momentum.

How do you solve for the velocities of the balls after the collision?

To solve for the velocities of the balls after the collision, you would need to use the principle of conservation of momentum. This means that the total momentum of the system before the collision is equal to the total momentum after the collision. By setting up and solving equations using the masses and initial velocities of the balls, you can determine the final velocities after the collision.

What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision. In an elastic collision, the objects involved bounce off each other without any loss of energy.

What factors affect the outcome of the Double Ball Drop experiment?

The outcome of the Double Ball Drop experiment is affected by several factors, such as the masses and initial velocities of the balls, the height from which they are dropped, and the surface on which they collide. Other factors that can also affect the outcome include air resistance, friction, and imperfections in the balls or the surface they collide on.

How is the Double Ball Drop experiment used in real-world applications?

The principles demonstrated in the Double Ball Drop experiment are used in various real-world applications, such as car safety and sports equipment design. Understanding elastic collisions and conservation of momentum helps in designing safer cars and sports equipment that can absorb and dissipate energy during collisions, reducing the impact on the people using them.

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