Using a lever, a person applies 60 N of force and moves the lever 1 m. This moves a 200 N rock at the other end by 0.2 m. What is the efficiency of the lever?
(200 N * 0.2 m) / (60 N * 1 m) = ?
Ah, the efficiency of the lever, let's crunch some numbers! Efficiency is all about bang for your buck, or in this case, work output compared to work input. To find the efficiency, we need to divide the useful work output by the work input and multiply by 100 to get a percentage.
So, the work input is the force multiplied by the distance, which gives us 60 N x 1 m = 60 N-m.
The work output is the force multiplied by the distance, which gives us 200 N x 0.2 m = 40 N-m.
Now, to calculate the efficiency, we divide the work output by the work input and multiply by 100: (40 N-m / 60 N-m) x 100 = 66.67%.
So, the efficiency of the lever is approximately 66.67%. Not too shabby, if you ask me!
To find the efficiency of the lever, we need to calculate the work input and the work output.
Work input (W_input) is the force applied multiplied by the distance moved.
W_input = Force * Distance
In this case, the force applied is 60 N and the distance moved is 1 m.
W_input = 60 N * 1 m = 60 Nm
Work output (W_output) is the force exerted by the rock multiplied by the distance the rock moves.
W_output = Force * Distance
In this case, the force exerted by the rock is 200 N and the distance it moves is 0.2 m.
W_output = 200 N * 0.2 m = 40 Nm
Efficiency (η) is calculated by dividing the work output by the work input and multiplying by 100 to express it as a percentage.
η = (W_output / W_input) * 100
Substituting the values we found earlier:
η = (40 Nm / 60 Nm) * 100 = 66.67%
Therefore, the efficiency of the lever is 66.67%.
To calculate the efficiency of the lever, we must first determine the input and output work done by the lever.
- Input work: The work done by the person applying the force on the lever.
- Output work: The work done by the lever on the rock.
The formula for calculating work is given by:
Work = Force × Distance
1. Calculate the input work:
Input Work = Input Force × Input Distance
Given:
Input Force = 60 N
Input Distance = 1 m
Input Work = 60 N × 1 m
Input Work = 60 N·m
2. Calculate the output work:
Output Work = Output Force × Output Distance
Given:
Output Force = 200 N
Output Distance = 0.2 m
Output Work = 200 N × 0.2 m
Output Work = 40 N·m
Now that we have calculated the input and output work, we can find the efficiency using the equation:
Efficiency = (Output Work / Input Work) × 100
Efficiency = (40 N·m / 60 N·m) × 100
Efficiency = (0.67) × 100
Efficiency = 67%
Therefore, the efficiency of the lever is 67%.