Physics - Elastic Collision: Solving for Unknowns

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SUMMARY

The discussion focuses on solving an elastic collision problem involving two balls of equal mass, where ball B has an initial velocity twice that of ball A. The angle of motion after the collision is calculated to be 26.3 degrees above the horizontal. The final velocity ratio of the combined mass A + B to the initial velocity of ball A is determined to be 1/3. Additionally, the ratio of the final energy of the system to the initial energy is also discussed, emphasizing the conservation of momentum and energy principles in elastic collisions.

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  • Understanding of elastic collision principles
  • Knowledge of vector decomposition in physics
  • Familiarity with trigonometric functions, specifically sine and cosine
  • Basic algebra for solving equations with multiple unknowns
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This discussion is beneficial for physics students, educators, and anyone interested in mastering concepts related to elastic collisions and momentum conservation in mechanics.

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Homework Statement



Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball B is twice that of ball A. (Take θ = 56°.)

(a) Calculate the angle above the horizontal of the motion of mass A + B after the collision.

(b) What is the ratio of the final velocity of the mass A + B to the initial velocity of ball A, vf/vA?

(c) What is the ratio of the final energy of the system to the initial energy of the system, Ef/Ei?

The Attempt at a Solution



a) x= m ( 2vcos(56) + vcos(56) ) = 2mVfx

2vcos(56) + vcos(56)= mvfx

y = m ( 2vsin(56) + vsin(56) ) = 2mVfy

2vsin(56) + vsin(56) = 2mVfy

Am I suppose to take the magnitude of this ? How do I solve for two unknowns ?
Do all the m's and v's cancel out?

Thanks
 

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y = m ( 2vsin(56) + vsin(56) ) = 2mVfy

2vsin(56) + vsin(56) = 2mVfy

There is something bad in the setup of the first equation.

Am I suppose to take the magnitude of this ? How do I solve for two unknowns ?
Do all the m's and v's cancel out?

Divide by the total mass of the body.
v remains.
 
2vcos(56) + vcos(56) = 2vfx => 3vcos(56)

2vsin(56) + -vsin(56) = 2vfy => vsin(56)

tan-1 ( y/x) => (1/3) => 26.3 degree
 

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