Question

# A cyclist and his bicycle has a mass of 80 kg. After 100m he reaches the top of a hill, with slope 1 in 20 measured along the slope, at a speed of 2 m/s. He then free wheels the 100m to the bottom of the hill where his speed has increased to 9m/s. How much energy has he lost on the hill?

A
844 J
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B
800 J
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C
860 J
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D
837 J
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Solution

## The correct option is A 844 J If the hill is 100 m long then the height is: h = 100120 = 5m So potential energy lost is mgh = 80×9.81×5 = 3924 J Increase in kinetic energy is 12mv2−12mu2 = 12m(v2−u2) = 40(81-4) = 3080 J By the principle of conservation of energy Initial energy = Final energy + loss of energy(due to friction etc.) loss of energy (due to friction etc.) = 3924 - 3080 = 844 J

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