a) In raising a 4800 N piano with a pulley system, the workers note that for every 2 m of rope pulled down, the piano rises 0.3 m. Ideally, how much force is required to lift the piano?
(b) If the workers actually pull with 2500 N of force to lift the piano, what is the efficiency of the pulley system?
%
MechanicalA= 2/.3
Force= 4800/MechA
Actual force*(efficiency)= forceneededabove
(a) To determine the force required to lift the piano using the pulley system, we need to calculate the mechanical advantage (MechA) of the system. The mechanical advantage is the ratio of the distance the force is exerted over the distance the load is moved.
In this case, the workers note that for every 2 m of rope pulled down, the piano rises 0.3 m. So the mechanical advantage can be calculated as:
MechA = distance force is exerted / distance load is moved
MechA = 2 m / 0.3 m
Now we can calculate the force required to lift the piano using the formula:
Force = weight of the piano / mechanical advantage
Force = 4800 N / MechA
Substituting the value of MechA calculated above:
Force = 4800 N / (2/0.3)
Simplifying:
Force = 4800 N / 6.6667
Therefore, the force required to lift the piano using the pulley system is approximately 720 N.
(b) If the workers actually pull with 2500 N of force to lift the piano, we can calculate the efficiency of the pulley system. Efficiency is the ratio of the useful work output to the work input.
The work input can be calculated by multiplying the force applied by the distance moved:
Work input = force applied * distance moved
The work output can be calculated by multiplying the weight of the piano by the distance it is raised:
Work output = weight of the piano * distance raised
Efficiency is given by the formula:
Efficiency = (work output / work input) * 100
Substituting the given values:
Work input = 2500 N * 2 m (distance the force is exerted)
Work output = 4800 N * 0.3 m (distance the load is moved)
Calculating the work input and work output:
Work input = 5000 J
Work output = 1440 J
Calculating the efficiency:
Efficiency = (1440 J / 5000 J) * 100
Therefore, the efficiency of the pulley system is approximately 28.8%.