An electric motor runs at a constant rotational frequency of 3000 r/min and has the load of

75 Nm and a 5,0 Nm extra load of friction and gear. The efficiency of the motor is 78%. a)
What is the input power of the motor? b) What is the work done by the motor in 24 hours
and c) what is the total electrical energy needed in 24 hours?

reherh

An electric motor runs at a constant rotational frequency of 3000 r/min and has the load of

75 Nm and a 5,0 Nm extra load of friction and gear. The efficiency of the motor is 78%. a)
What is the input power of the motor? b) What is the work done by the motor in 24 hours
and c) what is the total electrical energy needed in 24 hours?

To solve these questions, we will use the following formulas:

a) Input Power = Output Power / Efficiency
b) Work Done = Input Power × Time
c) Electrical Energy = Input Power × Time

Let's solve each part step-by-step:

a) Input Power:
First, we need to find the output power of the motor. The output power can be calculated using the formula:
Output Power = Torque × Angular Velocity

Given:
Rotational Frequency = 3000 r/min
Torque = 75 Nm

We need to convert the rotational frequency from r/min to rad/s:
Angular Velocity = Rotational Frequency × 2π/60

Substituting the values:
Angular Velocity = (3000 r/min) × (2π/60)
Angular Velocity = 100π rad/s

Now, we can calculate the output power:
Output Power = (75 Nm) × (100π rad/s)
Output Power = 7500π W

Next, we can calculate the input power using the formula for efficiency:
Input Power = Output Power / Efficiency

Given:
Efficiency = 78% = 0.78 (in decimal form)

Substituting the values:
Input Power = (7500π W) / 0.78
Input Power ≈ 30303.03π W

So, the input power of the motor is approximately 30303.03π W.

b) Work Done:
Given:
Time = 24 hours = 24 × 60 × 60 seconds

To calculate the work done, we use the formula:
Work Done = Input Power × Time

Substituting the values:
Work Done = (30303.03π W) × (24 × 60 × 60 seconds)
Work Done ≈ 825938526.6π J
(Note: This is an approximate value since π is irrational)

Therefore, the work done by the motor in 24 hours is approximately 825938526.6π J.

c) Electrical Energy:
To calculate the total electrical energy, we use the formula:
Electrical Energy = Input Power × Time

Substituting the values:
Electrical Energy = (30303.03π W) × (24 × 60 × 60 seconds)
Electrical Energy ≈ 825938526.6π J

Therefore, the total electrical energy needed in 24 hours is approximately 825938526.6π J.