A lift of mass 200kg moves upward with a uniform velocity of 4 m/s . if efficiency of motor is 70% then input power of motor is?
P = Fv = mgv
@70%
P = mgv/.7
To find the input power of the motor, we need to calculate the amount of power required to lift the mass at a constant velocity. The formula for power is:
Power = Force × Velocity
The force required to lift the mass can be calculated using the formula:
Force = Mass × Acceleration
Since the lift is moving upward with a uniform velocity, the acceleration is 0. Therefore, the force required is equal to the weight of the mass, which can be calculated using the formula:
Weight = Mass × Gravity
where Gravity is the acceleration due to gravity, approximately 9.8 m/s^2.
Given:
Mass = 200 kg
Velocity = 4 m/s
Efficiency = 70% (or 0.7)
Step 1: Calculate the weight of the mass:
Weight = Mass × Gravity
Weight = 200 kg × 9.8 m/s^2
Weight = 1960 N
Step 2: Calculate the force required to lift the mass:
Force = Weight
Force = 1960 N
Step 3: Calculate the power required to lift the mass:
Power = Force × Velocity
Power = 1960 N × 4 m/s
Power = 7840 W
Step 4: Calculate the input power of the motor, taking into account the efficiency:
Input Power = Power / Efficiency
Input Power = 7840 W / 0.7
Input Power ≈ 11,200 W (or 11.2 kW)
Therefore, the input power of the motor is approximately 11.2 kW.
To calculate the input power of the motor, we need to determine the work done by the motor and then divide it by the time it takes to do that work.
First, let's calculate the work done by the motor. Since the lift is moving upward with a uniform velocity, the net force acting on it is zero, meaning no work is being done against gravity. The only work done is against friction and other external factors, which we can assume to be negligible.
The formula for work (W) is given by:
W = force × distance
Since the lift is moving with a uniform velocity, we can calculate the force using the formula:
Force = mass × acceleration
In this case, since the lift is moving upward at a uniform velocity, the acceleration is zero. Thus, the force is also zero, and therefore, the work done by the motor is zero.
However, we know that the efficiency of the motor is 70%, which means that only 70% of the input power is converted into useful work. To calculate the input power, we can use the formula:
Efficiency = Useful work output / Input power
Since we know the efficiency is 70%, we can rearrange the formula to solve for the input power:
Input power = Useful work output / Efficiency
In this case, the useful work output is zero (as explained earlier), so the input power of the motor is also zero.
Therefore, the input power of the motor is zero in this scenario.