The actual mechanical advantage of a pulley is 2. The pulley has 3 supporting strings. What is the efficiency of the pulley?
The efficiency of a simple machine can be expressed as the ratio of the actual mechanical advantage divided by the theoretical mechanical advantage. You were given the actual mechanical advantage as 2, so you only need to determine the theoretical mechanical advantage. With a pulley system, this becomes a simple matter of determining how many strings support the pulley, which was nicely given as three. Therefore, the efficiency in this case is 2/3, or about 67%.
What could possibly have reduced the efficiency of this system to only 67%? I can think of a couple of possibilities: One, the pulley itself has some internal friction, but second, and more likely, the string moving over the pulley is producing a lot of friction and therefore reducing the useful work output.
The efficiency can also be found by taking the ratio of useful work output divided by total work input, which is an easier way to see how friction affects the system.