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25 November, 04:39

A 3047.8 kg truck has lost its brakes coming down a mountain. Fortunately, there is a ramp of thick gravel inclined at 9.5 degrees that the driver can use to stop the truck. The truck hits the ramp moving at 20.68 m/s and then travels 26.6 meters up the ramp before it comes to a stop. What work is done by the gravel to stop the truck?

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  1. 25 November, 04:51
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    The work done by the gravel to stop the truck is 520.44 kJ

    Explanation:

    Step 1: Data given

    Mass of the truck = 3047.8 kg

    The ramp has an angle of 9.5 °

    Velocity of the truck = 20.68 m/s

    distance = 26.6 meters

    Step 2: Calculate initial kinetic energy

    sin 9.5° = 0.165

    h = ℓ*sin 9.5° = 26.6*0.165 = 4.39 m

    Ek = 1/2m*Vo² = 1/2*3047.8*20.68² = 651714.7 Joule = 651.7 kJ = initial kinetic energy

    Step 3: Calculate potential energy

    Epot = U = m*g*h = 3047.8*9.81*4.39 = 131256.25 Joule = 131.26 kJ

    Step 4: What work is done by the truck on the gravel?

    Frictional energy Ef = 651.7 kJ - 131.26 kJ = 520.44 kJ
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