A cyclist and a bike have a combined mass of 100kg. The cyclist free-wheels (rolls without pedalling) at a constant speed of 0.8m/s down a 1 in 10 slope (this means that the cyclist descends 1.0m for each 10m travelled along the road, as shown in the diagram.) Calculate the loss in gravitational potential energy as he loses 100m in vertical height and hence calculate the total resistive force on the cyclist.

Answer:

23) D

Let us find the GPE when the cyclist is 100m in vertical height. Also, this is the amount of GPE that will be lost when the cyclist descends 100m.GPE = mgh = 100 x 10 x 100 = 100,000 J

To find the resistive force, we need to use the formula : Work done = Force x Distance
Rearranging to get Force, we get Force = Work done/Distance

In order to find the distance, we need to use the 1 in 10 information that is given to us.
We know that the cyclist descends 100m in vertical height.
Using the ratio of 1 : 10, we get 100 : 1000
So the distance travelled by the cyclist = 1000m

Work done is equal to the GPE lost by the cyclist.

Force = 100,000 ÷ 1000 = 100N