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?
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)
= 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