J Calculating Friction: Determining Energy Lost in Sled Ramp Descent

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A sled weighing 70 kg slides down a 3 m high ramp, initially traveling at 14 m/s and reaching a final velocity of 15.6 m/s. The energy lost due to friction is calculated using the equation .5mvi^2 + mgh = .5mvf^2 + x, where x represents the energy lost. The calculations show that the total energy before descent is 6860 J (kinetic) + 2058 J (potential), equaling 8918 J. After accounting for the final kinetic energy, the energy lost to friction is determined to be 401 J. However, the textbook indicates the correct answer is 74 J, suggesting a possible error in the calculations.
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Homework Statement



A sled weighing 70kg, going at 14 m/s, slides down a ramp 3 m high. It's final velocity is 15.6 m/s. How much energy was lost due to friction?


Homework Equations



.5mvi2 + mgh = .5mvf2 + x

where x = joules of energy for friction

The Attempt at a Solution



step 1 .5(70)(142+70(9.8)(3) = .5(70)(15.62 + x

step 2 6860 + 2058 = 8570 + x

step 3 6860 + 2058 - 8570 = x

step 4 401 = x

The books says the answer is 74
 
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I'd say that you were correct. (8570 is a typo, though.)
 

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