To determine the work lost to friction, we need to first calculate the work input and then calculate the work output. The difference between the work input and the work output represents the work lost to friction.
The work input is given by the formula:
Work input = Force × Distance
In this case, the force is the weight of the object being lifted, which is 20 N, and the distance is the height through which it is lifted, which is 10 m. Therefore:
Work input = 20 N × 10 m = 200 J
Next, we need to calculate the work output. The work output can be determined using the efficiency formula:
Efficiency = (Work output / Work input) × 100%
Given that the efficiency is 40% (or 0.4), we can rearrange the formula to solve for the work output:
Work output = Efficiency × Work input
Work output = 0.4 × 200 J = 80 J
Finally, we can calculate the work lost to friction:
Work lost to friction = Work input - Work output
Work lost to friction = 200 J - 80 J = 120 J
Therefore, the work lost to friction is 120 Joules.