Final answer:
The force required to lift the piano using the pulley system is 1000 N. The efficiency of the pulley system is 40%.
Step-by-step explanation:
To calculate the force required to lift the piano using the pulley system, we need to use the formula for mechanical advantage. Mechanical advantage is the ratio of output force to input force. In this case, the output force is the weight of the piano, which is 5000 N. The input force is the force applied by the workers.
Mechanical advantage = output force / input force = 5000 N / input force
Using the information given, for every 2m of rope pulled down, the piano rises 0.4m. So, the ratio of rope pulled down to the distance the piano rises is 2 / 0.4 = 5.
Therefore, the mechanical advantage is 5. Solving for the input force:
5000 N / input force = 5
Input force = 5000 N / 5 = 1000 N
So, ideally, a force of 1000 N is required to lift the piano using the pulley system.
To calculate the efficiency of the pulley system, we can use the formula: efficiency = (output work / input work) x 100%
Output work is the work done by the output force and is equal to the weight of the piano multiplied by the distance it is lifted. Input work is the work done by the input force and is equal to the force applied by the workers multiplied by the distance they move the rope down.
In this case, the output work is 5000 N * 0.4 m = 2000 N•m and the input work is 2500 N * 2 m = 5000 N•m.
Therefore, the efficiency of the pulley system is (2000 N•m / 5000 N•m) x 100% = 40%.