With the 0.02 kg mass gdanfling over the pulley, show by algebra how you would determine the work done ON the system
To determine the work done on the system, we need to calculate the work done by each force acting on the system.
First, let's list the forces acting on the system:
1. Force of gravity on the mass (mg)
2. Tension force in the rope (T)
The work done by each force can be calculated using the formula: W = F * d * cos(theta), where W is the work done, F is the magnitude of the force, d is the displacement, and theta is the angle between the force and the displacement.
1. Work done by the force of gravity:
The force of gravity acting on the mass is given by F_gravity = mg. Let's assume the displacement of the mass is h (height it moves up). The angle between the force of gravity and the displacement is 180 degrees (as they are in opposite directions). Therefore, the work done by the force of gravity is:
W_gravity = mg * h * cos(180)
Since cos(180) = -1, the work done by gravity simplifies to:
W_gravity = -mgh
2. Work done by the tension force in the rope:
The tension force in the rope is equal to the force required to lift the mass. So, T = mg. The displacement of the mass is again h, and the angle between the tension force and the displacement is 0 degrees (as they are in the same direction). Therefore, the work done by the tension force is:
W_tension = T * h * cos(0)
Since cos(0) = 1, the work done by the tension force simplifies to:
W_tension = mgh
To determine the total work done on the system, we add the work done by both forces:
Total work done = W_gravity + W_tension
= -mgh + mgh
= 0
Therefore, the total work done on the system is 0.