Calculating Motor Energy Consumption
This solution calculates the energy output of a motor based on its input power rating, efficiency, and operating time.
Given Parameters
- Motor Power Rating (Input, \(P_{in}\)): 2 kW
- Motor Efficiency (\(\eta\)): 80% or 0.8
- Time (\(t\)): 5 hours
Calculating Useful Output Power
The efficiency (\(\eta\)) relates the useful output power (\(P_{out}\)) to the input power (\(P_{in}\)):
\( \eta = \frac{P_{out}}{P_{in}} \)
To find the useful output power, rearrange the formula:
\( P_{out} = P_{in} \times \eta \)
Substitute the given values:
\( P_{out} = 2 \text{ kW} \times 0.8 = 1.6 \text{ kW} \)
This means the motor delivers 1.6 kW of useful power.
Calculating Energy Used (Output)
Energy used (in this context, the useful work done) is calculated by multiplying power by time:
\( \text{Energy} = P_{out} \times t \)
Substitute the calculated output power and the given time:
\( \text{Energy} = 1.6 \text{ kW} \times 5 \text{ hours} \)
\( \text{Energy} = 8 \text{ kWh} \)
Conclusion
The motor utilizes its input power and efficiency to deliver 8 kWh of energy over 5 hours.
Similar Questions
- The work done by a 10 Newton force acting on a body, which results in the displacement of 2 m in the direction of the force, is __________.
- An object of mass 1 kg is moving with a velocity 10 m/s. Find the kinetic energy of the object.
- The efficiency of a machine can never be ______.
- In practice, the work output of a machine is ______ the work input due to the effect of friction.
- A pump is required to lift 600 kg of water per minute from a well 25m deep and to eject it with a speed of 50 m/s. If \(g = 10 \text{ m/s}^2\), the power required to perform the above task is
- A lorry and a car moving with the same kinetic energy are brought to rest by applying the same retarding force. Then:
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Important Questions from Work Power and Energy
Which of the following is an example of potential energy?
_______ is one of the chemical used to produce Ocean Thermal Energy.
A body of mass 2kg is thrown up vertically with a kinetic energy of 500J. If the acceleration due to gravity is 10 m/s2, the height at which the kinetic energy of the body becomes half of the original values is _____
Arjun has a mass of 50 kg, he eats banana of 1000 calories. If this energy is used up to lift him from the ground, the height to which he can climb is _______. Take g = 10 m/s2 and 1 calories = 4.2 Joule.
When a body of mass 'm' attains a velocity 'v' from rest in time 't', then kinetic energy of translation is:
