What is the rate of energy transfer to the lift? Take g = 9.80 m/s².
Understand the Problem
The question is asking for the rate of energy transfer (power) to a lift moving at a constant velocity. It provides the mass of the lift and the acceleration due to gravity, indicating that we need to calculate the power using these values.
Answer
The rate of energy transfer to the lift is $18.1 \, \text{kW}$.
Answer for screen readers
The rate of energy transfer to the lift is $18.1 , \text{kW}$.
Steps to Solve
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Identify the formula for power To calculate the power required to lift the lift at a constant velocity, we use the formula: $$ P = F \cdot v $$ where ( P ) is the power, ( F ) is the force, and ( v ) is the velocity.
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Calculate the force required to lift the lift The force ( F ) is the weight of the lift, which can be calculated as: $$ F = m \cdot g $$ Substituting the values given: $$ F = 540 , \text{kg} \cdot 9.80 , \text{m/s}^2 $$
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Substitute values and calculate force Calculating the force gives: $$ F = 540 \cdot 9.80 = 5292 , \text{N} $$
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Calculate power using the velocity Now substituting ( F ) and ( v ) into the power equation: $$ P = 5292 , \text{N} \cdot 3.4 , \text{m/s} $$
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Perform the calculation for power Calculate ( P ): $$ P = 5292 \cdot 3.4 = 18080.8 , \text{W} $$
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Convert power from watts to kilowatts Since ( 1 , \text{kW} = 1000 , \text{W} ), convert the power: $$ P_{\text{kW}} = \frac{18080.8}{1000} = 18.1 , \text{kW} $$
The rate of energy transfer to the lift is $18.1 , \text{kW}$.
More Information
Power measures the rate at which energy is transferred. In this case, the lift requires a consistent input of energy to move upward against gravity.
Tips
- Forgetting to convert units: Ensure to convert watts to kilowatts by dividing by 1000.
- Miscalculating the force by neglecting either mass or gravitational acceleration.
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