Find mechanical energy lost when a cyclist goes down a hill

[Phys121VIU]

A cyclist has a speed of 5 m/s when she beings to coast down a hill, as shown in the figure. At the bottom of the hill, her speed has increased to 12m/s. the mass of the cyclist plus bicycle is 75kg.

a) Calculate the work done by gravity on the cyclist and bicycle.

b) Calculate the mechanical energy lost because of air resistance and friction. Explain.


I found the work done(part a):

Work = ΔK = K_f - K_i

Work = [(1/2)mv_f² - (1/2)mv_i²]

Work = [(1/2)(75kg)(12m/s)² - (1/2)(75kg)(5m/s)²]

Work = (5400 - 937.5)Nm = J

Work = 4463 J


What I don't understand is how to find the air resistance and friction..i just need an idea of where to start


Thanks!

 

[mishek]

What is the calculated work used for?

What speed would cyclist have when there would be no need to do work?

 

[Phys121VIU]

Gravity? I'm not sure what your asking..

 

[mishek]

Let's say there would be no need to do any work. In that way, you would only have exchange between kinetic and potential energy. On top of the hill, your PE would be max and your KE would be min. On bottom of the hill, your KE would be max and your PE would be min. But such exchange is not possible because you have some losses and you need to do some work. Now I see that you neglected the potential energy.

 

[Nickie]

To find the mechanical energy lost due to air resistance and friction, we need to first understand the concept of mechanical energy. Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (energy due to position or height). In this scenario, the cyclist starts with a certain amount of mechanical energy (kinetic and potential) at the top of the hill, and at the bottom of the hill, the mechanical energy has changed due to the work done by gravity.

To find the mechanical energy lost, we can use the conservation of energy principle, which states that energy can neither be created nor destroyed, it can only be transferred from one form to another. In this case, the mechanical energy lost will be equal to the work done by gravity minus the work done by the cyclist's legs to maintain a constant speed.

Therefore, to find the mechanical energy lost, we need to first calculate the work done by the cyclist's legs, which is equal to the change in kinetic energy (ΔK) as the speed remains constant. This can be calculated using the formula ΔK = (1/2)mvf2 - (1/2)mvi2, where vf is the final speed (12m/s) and vi is the initial speed (5m/s).

Next, we can calculate the work done by gravity, which we have already calculated in part a as 4463 J.

Finally, to find the mechanical energy lost, we can subtract the work done by the cyclist's legs from the work done by gravity. This difference will give us the work done by air resistance and friction, as these factors will have caused a decrease in the cyclist's mechanical energy. This work done by air resistance and friction can be converted to Joules (J) and will give us the mechanical energy lost.

In summary, to find the mechanical energy lost, we need to use the conservation of energy principle and calculate the work done by gravity and the work done by the cyclist's legs. The difference between these two values will give us the work done by air resistance and friction, which can be converted to Joules to find the mechanical energy lost.