Question

A cyclist intends to cycle up a 7.20∘ hill whose vertical height is 145 m. The pedals turn in a circle of diameter 39.0 cm. Assuming the mass of bicycle plus person is 95.0 kg, calculate how much work must be done against gravity.

Answer 1

The cyclist must do approximately 135576.75 Joules of work against gravity to reach the top of the hill with a vertical height of 145 m, with a combined mass of the bicycle and the cyclist being 95.0 kg.

Step-by-step explanation:

To calculate the work done against gravity by a cyclist intending to cycle up a 7.20° hill with a vertical height of 145 m, we need to use the work-energy principle. The work done by gravity is equal to the change in gravitational potential energy. We can calculate this as Work (W) = mass (m) × gravitational acceleration (g) × height (h).

The mass of the cyclist and the bicycle combined is 95.0 kg, and the height they need to rise is 145 meters. Assuming the value of gravitational acceleration (g) as 9.81 m/s², the calculation becomes:

Work = 95.0 kg × 9.81 m/s² × 145 m

When we multiply these numbers, we get:

Work = 135576.75 Joules

So, the cyclist must do approximately 135576.75 Joules of work against gravity to reach the top of the hill.