A 62kg cyclist changes the speed of a 12kg bicycle from 8.2m/s to 12.7m/s. Determine the work done.
I've already answered & gotten this question correct, however it made me confused about the concept.
I found Ek. & Ek to find change in Ek which was 3479.85. He did work against both friction & inertia & yet this one formula covered both & I didn't have to add anything together. Why not? As far as I understood, to get Work total you need to do the formula for each work (friction & inertia) then add.
Thank you!! ☺
No, the work done was the difference in kinetic energies, assuming the work to overcome friction at each speed was constant.
So does that mean if I have work against friction & acceleration I can use that one formula to cover both? :)
Yes, if the friction involved in attaining different speeds was the same....in real life, it is not. Friction of air is dependent on velocity squared as a rule of thumb.
Ok, that's super helpful thank you very much!! :)
To determine the work done in this scenario, you are correct that you need to consider both the work done against friction and the work done against inertia. However, in this particular case, you can use a single formula to calculate the total work done.
Let's break it down step by step:
1. Start by calculating the initial kinetic energy (Ek) of the cyclist-bicycle system. The formula for kinetic energy is Ek = 0.5 * mass * velocity^2. Since the cyclist's mass is 62 kg and the initial velocity is 8.2 m/s, we have Ek_initial = 0.5 * 62 kg * (8.2 m/s)^2.
2. Next, calculate the final kinetic energy (Ek) of the system. The cyclist's mass remains the same at 62 kg, but the final velocity is 12.7 m/s. Thus, Ek_final = 0.5 * 62 kg * (12.7 m/s)^2.
3. Now, determine the change in kinetic energy (ΔEk) by subtracting the initial kinetic energy from the final kinetic energy: ΔEk = Ek_final - Ek_initial.
In this case, you correctly calculated that ΔEk = 3479.85 J. This represents the total change in kinetic energy of the system.
4. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Therefore, the work done in this scenario is equal to the change in kinetic energy: Work_total = ΔEk.
The reason you don't need to separately consider the work done against friction and the work done against inertia is because they are both accounted for in the change in kinetic energy. Friction opposes the motion of the cyclist-bicycle system, reducing its kinetic energy, while inertia represents the resistance to a change in velocity. By calculating the change in kinetic energy, you are effectively incorporating both of these factors into a single value.
So, in summary, to find the total work done in this scenario, you can use the formula Work_total = ΔEk, where ΔEk is the change in kinetic energy.