Calculating Work Done by Air Resistance on a Thrown Ball

[Elysium]

Hi, I'm having problems with this question:

2. A 0.63-kg ball is thrown straight up into the air with an initial speed of 14 m/s. It reaches a height of 8.1 m, then falls back down. Assume that the only forces acting are those of gravity and air resistance and calculate the work done during the ascent by the force of air resistance. (Hint: Use the CWE theorem and the potential energy associated with the gravitational work.)

ok first I determined what work that gravtity does which is m*g*(delta y) which in this case is -50 J

I then used the CEW theorem equation using the velocities to find the total work done: (sigma W) = 1/2 m (v^2 (final) - v^2(initial)) which is -62 J

Last part is that I used the relationship between the work of gravity and the total work (sigma)W = W of gravity + Work of air resistance. I got -12 Joules for air resistance. I don't know but I feel like I got something wrong here. Can anyone help me out?

 

[verty]

Well, the difference between the kinetic energy at the bottom and the potential energy at the top will be the amount lost due to air resistance.

E_a = (1/2)mv^2 - mgh = 61.7 - 50
= 11.7J

W_a = E_a
= 11.7J

I don't know the method you have used.

Edit: Work is a scalar I see.

 

[quicknote]

Hi there,

Thank you for sharing your work and question with me. It seems like you have a good understanding of the concepts involved in calculating work done by air resistance on a thrown ball. Let me provide some additional insights that may help clarify any confusion.

First, it is important to note that the work done by air resistance is always negative, as it acts in the opposite direction of the motion. In this case, as the ball is thrown upwards, the air resistance is acting downwards, so the work done by air resistance will be negative.

Next, your calculation for the work done by gravity is correct. However, the calculation for the total work done using the CEW theorem should be -50 J, not -62 J. This is because the initial and final velocities are the same (both 14 m/s) since the ball starts and ends at the same height. Therefore, the net work done by all forces should be equal to the work done by gravity, which is -50 J.

To calculate the work done by air resistance, you can use the same equation you used for the total work done, but use the final and initial velocities for the air resistance force. Since the ball is moving upwards, the air resistance force will be in the opposite direction, so the final velocity will be 0 m/s and the initial velocity will be 14 m/s. This will give you a work done by air resistance of -49 J.

Finally, to find the work done by air resistance during the ascent, you can subtract the work done by gravity (-50 J) from the total work done (-50 J). This will give you a final answer of -1 J for the work done by air resistance during the ascent of the ball.

I hope this helps clarify your calculations. Keep up the good work!