Conservation of energy problem

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SUMMARY

The conservation of energy problem involves a ball thrown downward with an initial velocity of 5.0 m/s from a height of 8.0 m. Using the equations for kinetic energy (K = 1/2 mv²) and gravitational potential energy (U = mgh), the speed of the ball upon impact with the base of the track can be calculated without needing the mass, as it cancels out in the energy conservation equation. The ball then travels up a frictionless ramp, reaching a height determined by the conservation of mechanical energy principles.

PREREQUISITES
  • Understanding of kinetic energy and potential energy equations
  • Familiarity with the concept of conservation of mechanical energy
  • Basic knowledge of projectile motion
  • Ability to manipulate algebraic equations
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  • Study the derivation of the conservation of energy principle in physics
  • Learn how to apply energy conservation in different scenarios, including frictionless surfaces
  • Explore the implications of mass cancellation in energy equations
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1. a student throws a ball down with an initial velocity of 5.0 m/s from a point 8.0 m above the base of a track. Find the speed of the ball as it hits the base of the track. The track is designed to losslessly change the direction of the ball up a frictionless ramp. What is the height above the ground reached by the ball



2. K = 1/2 mv^2
U = mgh
E1 = E2




3. If I knew the mass of the ball this problem would be easy
U = mgh
K= 1/2 mv^2
mgh(initial) + 1/2mv^2(initial) = mgh(final)
I don't have the mass
is there an equation that I can sub into the above to isolate the mass or is mass irrelevant as it is on both sides of the equation?

 
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Well, of course if the mass is on both sides of the equation, it cancels
 

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