Conservation of energy problem

AI Thread Summary
To solve the conservation of energy problem, the initial kinetic energy (K) and potential energy (U) of the ball must be considered. The equations K = 1/2 mv^2 and U = mgh are used to establish energy conservation, where the total energy at the initial height equals the total energy at the final height. Since mass appears on both sides of the energy equation, it cancels out, making it irrelevant for calculating the final speed and height. The final speed of the ball as it hits the base can be determined using the initial velocity and height, while the maximum height reached after the ramp can be calculated using energy conservation principles. The discussion emphasizes that mass does not affect the outcome in this context.
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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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