elbow raises a 1200 N piano a distance of 5 meters using a set of pulleys. elbow pulls in 20.0 meter of rope while exerting a force of 340 N.
a) what is the work output?
b) what is work input
c) what is the mechanical advantage of this machine?
d) what is the efficiency of this machine?
work output=1200*5
work input=20*340
MA=1200/340
To calculate the various quantities in this scenario, we need to use the formulas for work, force, distance, mechanical advantage, and efficiency.
a) Work Output:
Work = Force × Distance
In this case, the work output is the work done by the elbow to raise the piano. The force exerted by the elbow is 1200 N, and the distance over which the piano is raised is 5 meters.
Work Output = 1200 N × 5 m = 6000 N·m (or Joules)
b) Work Input:
Work = Force × Distance
The work input refers to the work done by the elbow in pulling the rope. The force exerted by the elbow is 340 N, and the distance over which the elbow pulls the rope is given as 20.0 meters.
Work Input = 340 N × 20.0 m = 6800 N·m (or Joules)
c) Mechanical Advantage:
Mechanical Advantage (MA) = Force Output / Force Input
In this case, the force output is the force required to lift the piano, which is 1200 N, and the force input is the force exerted by the elbow, which is 340 N.
Mechanical Advantage = 1200 N / 340 N = 3.53 (rounded to two decimal places)
d) Efficiency:
Efficiency = (Work Output / Work Input) × 100%
Efficiency measures how well a machine converts input work to useful output work. It is represented as a percentage.
Efficiency = (6000 N·m / 6800 N·m) × 100% = 88.24% (rounded to two decimal places)
By applying the formulas correctly, we have calculated the work output, work input, mechanical advantage, and efficiency of the given machine.
To calculate the values you mentioned, we'll use the following formulas:
a) Work output = Force output * Distance output
b) Work input = Force input * Distance input
c) Mechanical Advantage = Force output / Force input
d) Efficiency = (Work output / Work input) * 100
Given information:
Force output (FO) = 1200 N
Distance output (DO) = 5 m
Force input (FI) = 340 N
Distance input (DI) = 20.0 m
a) Work output = FO * DO
Work output = 1200 N * 5 m = 6000 N·m or J
b) Work input = FI * DI
Work input = 340 N * 20.0 m = 6800 N·m or J
c) Mechanical Advantage = FO / FI
Mechanical Advantage = 1200 N / 340 N = 3.53 (approx.)
d) Efficiency = (Work output / Work input) * 100
Efficiency = (6000 N·m / 6800 N·m) * 100 = 88.24% (approx.)
Therefore:
a) The work output is 6000 N·m or J.
b) The work input is 6800 N·m or J.
c) The mechanical advantage of this machine is approximately 3.53.
d) The efficiency of this machine is approximately 88.24%.