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
• B. 800 J
• C. 860 J
• D. 837 J

Answer 1

The correct option is A 844 J

If the hill is 100 m long then the height is: $h=100\frac{1}{20}=5m$
So potential energy lost is $mgh=80\times 9.81\times 5=3924J$
Increase in kinetic energy is $\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2=\frac{1}{2}m(v^2-u^2)$
= 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