The efficiency of a maching is 80%.determine the workdone by a person using his machine to raise a load of 200kg through a vertical distance of 3.0m.take g(10m/s)show full working.
increase of potential energy = m g h = 200 * 10 * 3 = 6,000 Joules
6,000 /0.80 = 7500 Joules
To determine the work done by a person using a machine, we need to calculate the input work and then adjust it for the efficiency of the machine.
Given:
Efficiency of the machine (η) = 80% = 0.8
Load (m) = 200 kg
Vertical distance (h) = 3.0 m
Acceleration due to gravity (g) = 10 m/s²
Step 1: Calculate the potential energy of the load.
Potential energy (PE) = m * g * h
PE = 200 kg * 10 m/s² * 3.0 m
PE = 6000 J
Step 2: Calculate the input work.
Input work (W_input) = PE / η
W_input = 6000 J / 0.8
W_input = 7500 J
Therefore, the work done by a person using the machine to raise the load of 200 kg through a vertical distance of 3.0 m is 7500 J.
To determine the work done by a person using the machine, you need to calculate the input work and then multiply it by the machine's efficiency. Here's how you can do it:
1. Calculate the input work:
Input work = force x distance
Given:
Mass (m) = 200 kg
Acceleration due to gravity (g) = 10 m/s^2
Distance (d) = 3.0 m
Force (F) = m x g (using Newton's second law)
Substituting the given values:
F = 200 kg x 10 m/s^2
= 2000 N
Input work = F x d
= 2000 N x 3.0 m
= 6000 Nm (or Joules)
2. Calculate the work done by the person using the machine:
Work done by the person = Input work x Efficiency
Given:
Efficiency = 80% = 0.80 (as a decimal)
Work done by the person = 6000 Nm x 0.80
= 4800 Nm (or Joules)
Therefore, the work done by the person using the machine to raise a load of 200 kg through a vertical distance of 3.0 m is 4800 Nm (or Joules).