This is a question related to work.

Today we had a pop quiz in my physics class and I am just trying to check my work here :D
1)
if there is a 5 kg block on a horizontal table connected with string to a 3 kg block hanging off the side of the table through a pulley. Assume the string is weightless and friction is neglectable in the system.

if the 5kg block moved .5 meters without any external force/pushing. What is the work done to the system?

I got:
work done = Net force * displacement
= (3kg*9.8)*(0.5)
= 14.7 Joules//

2)
assume some condition and displacement in part 1, what is the net work on the system if there is a friction Coefficient of 0.25 between the table and the 5kg block?

It would just be the 14.7 - (0.25*normal F)(0.5) of 5kg block right?
so the ans will be
14.7- 6.125
= 8.575 Joules//

To check your work for both questions, let's go through them step by step:

1) For the first question, you correctly calculated the work done to the system. The work done is given by the formula: work done = Net force * displacement. In this case, the net force is equal to the force due to the weight of the hanging block (3 kg * 9.8 m/s^2), and the displacement is given as 0.5 meters. Therefore, the work done is (3 kg * 9.8 m/s^2) * 0.5 meters = 14.7 Joules.

2) For the second question, you are considering the presence of friction between the table and the 5 kg block. The net work on the system can be calculated by subtracting the work done against friction from the initial work done. The work done against friction is given by the formula: work done against friction = friction force * displacement. The friction force can be calculated as the product of the coefficient of friction (0.25) and the normal force acting on the 5 kg block. The normal force is the force exerted by the table on the block and is equal to the weight of the block (5 kg * 9.8 m/s^2). The displacement remains the same (0.5 meters). Therefore, the work done against friction is (0.25 * 5 kg * 9.8 m/s^2) * 0.5 meters = 6.125 Joules. Subtracting this from the initial work done (14.7 Joules - 6.125 Joules), the net work on the system is 8.575 Joules.

Overall, your calculations for both questions are correct. Well done!