Conservation of kinetic energy/linear momentum problem

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SUMMARY

The discussion focuses on a physics problem involving an 8-kg sphere A colliding with a 10-kg block B on a 45° inclined surface. The initial conditions state that sphere A moves left at 15 m/s while block B moves right at 5 m/s. The impact is perfectly elastic, requiring the application of conservation of kinetic energy and linear momentum equations to determine the final velocities of both objects after the collision. The key challenge identified is resolving the velocity of the inclined block into its horizontal component for accurate calculations.

PREREQUISITES
  • Understanding of conservation of kinetic energy principles
  • Knowledge of linear momentum conservation
  • Ability to resolve vectors, particularly on inclined planes
  • Familiarity with elastic collision concepts
NEXT STEPS
  • Study vector resolution techniques for inclined surfaces
  • Learn about perfectly elastic collisions and their mathematical implications
  • Review examples of conservation of momentum in two-dimensional collisions
  • Explore the application of kinetic energy conservation in collision problems
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Students studying physics, particularly those focusing on mechanics and collision problems, as well as educators seeking to enhance their teaching of elastic collisions and momentum conservation.

jhahler
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Homework Statement


An 8-kg sphere A is moving to the left with a velocity of 15 m/s when it strikes the 45° inclined surface of a 10-kg block B which is moving to the right a 5 m/s. The ball strikes the block 1 meter above the ground. The block is supported by rollers and impact is perfectly elastic. Determine the speeds of A and B after the impact.


Homework Equations


1/2mb(vb)^2 + 1/2ma(va)^2 = 1/2mb(vb)^2 + 1/2ma(va)^2 (initial kin. energy = final kin. energy)
mbvb + mava = mbvb + mava (initial linear mom. = final linear mom.)

The Attempt at a Solution


I know to use those 2 equations to solve for the 2 unknowns Vb final and Va final, but the only thing that's messing me up is what to do with the 45° incline on the block, and I think that the ball striking the block 1 foot about the ground is irrelevant, but I'm not positive. Any help is much appreciated.
 
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Try and resolve the 'v' of the inclined block into its horizontal component. And then put the derived 'v' into the equation.
 

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