Oblique Impact of Smooth Spheres

AI Thread Summary
The discussion revolves around a physics problem involving the oblique impact of two spheres, where one sphere of mass m collides with another stationary sphere of mass M, and the coefficient of restitution is e. The key equation derived indicates that if m equals eM, the velocities after impact can be expressed in terms of their components. The user struggles with the interpretation of the equations and the need to consider directional components to demonstrate that the motion directions post-impact are perpendicular. The conversation highlights the importance of analyzing both x and y components to solve the problem effectively. Understanding these components is crucial for proving the right-angle relationship between the directions of motion after the impact.
SpartaGhost
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Hey, I'm struggling with this question, any help would be great.

A sphere of mass m impinges obliquely on a sphere of mass M, which is at rest. The coefficient of restitution between the spheres is e. Show that if m=eM, the directions of motion after impact are at right angles

My attempt was:

mUcosα = mV1 + MV2 (1)
V2-V1 = e(Ucosα) (2)

since m=eM
=> eMcosα = eMV1 + Mv2 then /m

so subtracting the equations gives
eUcosα = eV1 + V2
- eUcosα = V2 - V1

=> 0 = eV1 + V1
e = -1

which is where I just don't understand what to do now :(
 
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Well, if you want to show that " the directions of motion after impact are at right angles" you had better work with the directions of motion hadn't you? Yet, I see no indication of x or y components. You see to be treating V1 and V2 as numbers- that is, assuming the two masses move in a straight line.
 
Hi, I used the parallel and perpendicular components and yeah the masses move in a linear direction.
 

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