Proving Perpendicular Motion of Two Colliding Spheres

In summary, two spheres of masses km and m collided obliquely with a coefficient of restitution of 1/k (k greater or equal to 1). The sphere of mass m was brought to rest by the impact. Before the collision, the spheres were moving perpendicular to each other. It has been proven that k=-1 and the sphere of mass m had initial momentum of xi+0j and final momentum of 0i+0j. It has also been shown that as a result of the collision, the kinetic energy lost by the sphere of mass m is k times the kinetic energy gained by the sphere of mass km, with the kinetic energy lost by mass m being .5mx^2 and the kinetic energy gained by mass
  • #1
markosheehan
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Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other.

i have worked out k=-1. I know the sphere of mass m was xi+0j before and 0i+0j after.
 
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  • #2
i have worked out the first part
the second part of the question is show that as a result of the collision the kinetic energy lost by the sphere of mass m is k times the kinetic energy gained by the sphere of mass km.
the kinetic energy lost by mass m sphere is .5mx^2
kinetic energy gained by mass km sphere is .5(km)(y)^2-.5(km)(a)^2
Any help?
 

FAQ: Proving Perpendicular Motion of Two Colliding Spheres

What is the purpose of proving perpendicular motion of two colliding spheres?

The purpose of proving perpendicular motion of two colliding spheres is to demonstrate the principle of conservation of momentum and energy in a two-dimensional collision scenario. This can help us understand the behavior of objects in motion and how they interact with each other.

How can we prove that the motion of two colliding spheres is perpendicular?

To prove perpendicular motion, we can use a setup where two spheres of equal mass and size collide on a smooth, flat surface. By analyzing the motion of the spheres before and after the collision and using equations of motion, we can calculate the angles of their paths and determine if they are perpendicular.

What factors can affect the perpendicular motion of two colliding spheres?

The main factors that can affect perpendicular motion are the masses, velocities, and angles of the spheres before the collision. Other factors such as external forces, friction, and surface conditions can also play a role.

Why is it important to prove perpendicular motion in two-sphere collisions?

Proving perpendicular motion in two-sphere collisions is important because it is a fundamental concept in physics that helps us understand and predict the behavior of objects in motion. It also has practical applications in fields such as engineering and mechanics.

Can perpendicular motion occur in three or more-sphere collisions?

Yes, perpendicular motion can occur in three or more-sphere collisions as long as the spheres are arranged and colliding in a way that allows for perpendicular paths. However, it may be more complex to prove and analyze compared to two-sphere collisions.

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