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M2 Energy/Work question
Hi,
Would anybody be able to solve the below problem for me? I'm having trouble getting the correct result, and need to see how to go about approaching this type of questions.
A cyclist starts from rest and freewheels down a hill inclined at arcsin 1/20 to the horizontal. After travelling 80m the road becomes horizontal and the cyclist reavels anothing 80m before coming to rest without using his brakes. Given that the mass of the cyclist and his machine is 80kg, find the resistive force, assumed constant throughout this motion.
Your help is much appreciated.
Matt
Would anybody be able to solve the below problem for me? I'm having trouble getting the correct result, and need to see how to go about approaching this type of questions.
A cyclist starts from rest and freewheels down a hill inclined at arcsin 1/20 to the horizontal. After travelling 80m the road becomes horizontal and the cyclist reavels anothing 80m before coming to rest without using his brakes. Given that the mass of the cyclist and his machine is 80kg, find the resistive force, assumed constant throughout this motion.
Your help is much appreciated.
Matt
Set potential energy = 0 at the height of the horizontal piece of road.
Let m = 80 kg,
h = height of the cyclist's starting point.
s = 160m = total travelled distance
F = resistive force
We have that h/(80m) = sin arcsin(1/20) and so h = 4m.
Initially, the kinetic energy of the cyclist + cycle is 0, and the potential energy is mgh. After the cyclists have come to rest again, the kinetic energy is again 0, and the potential energy is 0 as well. The cyclist has thus lost mgh in energy, from the work done by the resitive force, and we have
mgh = Fs
F = mgh/s
Let m = 80 kg,
h = height of the cyclist's starting point.
s = 160m = total travelled distance
F = resistive force
We have that h/(80m) = sin arcsin(1/20) and so h = 4m.
Initially, the kinetic energy of the cyclist + cycle is 0, and the potential energy is mgh. After the cyclists have come to rest again, the kinetic energy is again 0, and the potential energy is 0 as well. The cyclist has thus lost mgh in energy, from the work done by the resitive force, and we have
mgh = Fs
F = mgh/s
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