A 62kg cyclist changes the speed of a 12kg bicycle from 8.2m/s to 12.7m/s. Determine the work done.
I used change in energy = work to find work against inertia which was 3479.85
Then I used V^2=V.^2 + 2ad to get ad=47.025
I then used W=mad to get work against friction, my problem is that was also 3479.85...
What am I doing wrong?
Thank you! ☺
the work calculation is the total work
the components are not separable
... not enough information
What I understood was that Wtotal=the sum of all work, but is what I did maybe Wtotal?
It seems like you are on the right track with your calculations, but there might be a slight error in one of your steps. Let's go through the problem again and see where things might have gone wrong.
To find the work done, we can consider the work against inertia and the work against friction separately.
First, let's calculate the work against inertia. We can use the formula:
Work = Change in kinetic energy
Given:
Mass of the cyclist (m1) = 62 kg
Mass of the bicycle (m2) = 12 kg
Initial velocity (v1) = 8.2 m/s
Final velocity (v2) = 12.7 m/s
Change in kinetic energy (ΔKE) = 1/2(m1 + m2)(v2^2 - v1^2)
Substituting the given values into the formula:
ΔKE = 1/2(62 + 12)(12.7^2 - 8.2^2)
Calculating this gives us:
ΔKE = 1/2(74)(162.09 - 67.24)
= 1/2(74)(94.85)
= 3477.35 J (approximately)
So, the work done against inertia is approximately 3477.35 J.
Now, let's calculate the work done against friction. You used the equation W = mad, where 'm' is the mass, 'a' is the acceleration, and 'd' is the distance.
However, in this case, we don't have the information about the acceleration or the distance. So, we need to find another approach to calculate the work done against friction.
One possible method is to use the idea that the net work done is equal to the change in kinetic energy. Since we have already calculated the work done against inertia (which accounts for the change in kinetic energy), we can subtract it from the total work done to find the work done against friction:
Total work done = Work against inertia + Work against friction
Using this equation, we can solve for the work done against friction:
Work against friction = Total work done - Work against inertia
= 3479.85 J (from your calculations) - 3477.35 J (initially calculated)
= 2.5 J
So, the work done against friction is approximately 2.5 J.
To recap, the work done against inertia is approximately 3477.35 J, and the work done against friction is approximately 2.5 J.