The power of a lever used to raise a 50-kg load a height of 10 m in 5 s is:
Understand the Problem
The question is asking to calculate the power of a lever used to raise a 50-kg load a height of 10 meters in 5 seconds. The key concepts involve understanding the formulas for power, which is calculated as work done over time.
Answer
$0.981 \, \text{kW}$
Answer for screen readers
The power of the lever is approximately $0.981 , \text{kW}$.
Steps to Solve
- Calculate the Work Done
To calculate work done ($W$), use the formula: $$ W = mgh $$ Where:
- $m = 50 , \text{kg}$ (mass of the load)
- $g = 9.81 , \text{m/s}^2$ (acceleration due to gravity)
- $h = 10 , \text{m}$ (height)
Plugging in the values: $$ W = 50 \times 9.81 \times 10 $$
- Calculate the Power
Power ($P$) is calculated as work done over time. The formula for power is: $$ P = \frac{W}{t} $$ Where:
- $t = 5 , \text{s}$ (time).
Using the work done from the previous step: $$ P = \frac{W}{5} $$
- Compute the Final Values
First, calculate the work done: $$ W = 50 \times 9.81 \times 10 = 4905 , \text{J} $$
Now, use this to find the power: $$ P = \frac{4905}{5} = 981 , \text{W} $$
Convert this to kilowatts: $$ P = \frac{981}{1000} = 0.981 , \text{kW} $$
The power of the lever is approximately $0.981 , \text{kW}$.
More Information
In practical terms, this means that the lever exerts almost 1 kW of power while lifting the load. Power is a crucial concept in mechanics, signifying how efficiently work is done over time.
Tips
- Forgetting to convert watts to kilowatts by dividing by 1000.
- Not considering the acceleration due to gravity in the work calculation.
- Using incorrect units; ensure mass is in kilograms, height in meters, and the result in watts.
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