To answer this question, we need to consider the energy transfers occuring at each stage. At the start, the cyclist has no kinetic energy, so her kinetic energy at the bottom can be calculated by taking her loss in gravitational potential energy (Mass * g * height travelled) and deducting any losses due to friction. As the question has stated that the losses due to friction are 15 percent of her total energy, we can work out the kinetic energy at the bottom of the hill to be 85 percent of the gravitational potential energy she lost.
Since the question states that we can assume there are no energy losses after she cycles downhill, we can work out her kinetic energy at the top of the next hill (0.5 * mass * velocity^2) and subtract this from her kinetic energy at the bottom of the hill to get the difference in kinetic energy.
Difference in kinetic energy = total work done - gravitiational potential energy gained while cycling up the hill
We can work out the gravitational potential energy she gains after cycling up the hill using the height and substitute this into our equation to obtain the total work she does in cycling up the hill.
I hope this helps! Please let me know if you have any further questions.
Hi @Apaul466,
To answer this question, we need to consider the energy transfers occuring at each stage. At the start, the cyclist has no kinetic energy, so her kinetic energy at the bottom can be calculated by taking her loss in gravitational potential energy (Mass * g * height travelled) and deducting any losses due to friction. As the question has stated that the losses due to friction are 15 percent of her total energy, we can work out the kinetic energy at the bottom of the hill to be 85 percent of the gravitational potential energy she lost.
Since the question states that we can assume there are no energy losses after she cycles downhill, we can work out her kinetic energy at the top of the next hill (0.5 * mass * velocity^2) and subtract this from her kinetic energy at the bottom of the hill to get the difference in kinetic energy.
Difference in kinetic energy = total work done - gravitiational potential energy gained while cycling up the hill
We can work out the gravitational potential energy she gains after cycling up the hill using the height and substitute this into our equation to obtain the total work she does in cycling up the hill.
I hope this helps! Please let me know if you have any further questions.
"Difference in kinetic energy = total work done - gravitiational potential energy gained while cycling up the hill"
Where did you derive this from? Why do you need to calculate the DIFFERENCE in K.E?
Many thanks for this!