A 2.6x10^3 kg elevator carries a maximum load of 888.1 kg. A constant frictional force of 4.9x10^3 N s the elevator's motion upward. The acceleration of gravity is 9.81 m.s^2.
What minimum power must the motor deliver to lift the fully loaded elevator at a constant speed 2.49 m/s?
Answer in units of kW
[(Fully loaded mass)*g + (Friction force]*V = Power required
To determine the minimum power the motor must deliver to lift the fully loaded elevator at a constant speed of 2.49 m/s, we need to consider the various forces acting on the elevator.
1. Weight of the elevator: The weight of the elevator can be calculated by multiplying its mass (2.6x10^3 kg) by the acceleration due to gravity (9.81 m/s^2). This will give us the force required to counteract the gravitational pull, which is equal to 2.6x10^3 kg * 9.81 m/s^2.
2. Frictional force: The frictional force opposing the elevator's motion is given as 4.9x10^3 N and acts in the upward direction.
3. Net force: The net force on the elevator should be zero since it is moving at a constant speed. Therefore, the force exerted by the motor must balance the sum of the weight and frictional force.
Now, let's calculate the minimum power required by the motor using the following equation:
Power = Force * Velocity
First, we need to find the net force acting on the elevator. It can be determined by summing the weight and frictional force:
Net force = Weight - Frictional force
Next, we can calculate the minimum power using the equation:
Power = Net force * Velocity
Finally, we'll convert the power from watts to kilowatts:
Power (kW) = Power (W) / 1000
Let's calculate the answer:
Step 1: Calculate the weight of the elevator:
Weight = Mass * Acceleration due to gravity
Weight = 2.6x10^3 kg * 9.81 m/s^2
Step 2: Calculate the net force on the elevator:
Net force = Weight - Frictional force
Step 3: Calculate the minimum power required:
Power = Net force * Velocity
Step 4: Convert the power to kilowatts:
Power (kW) = Power (W) / 1000
Plug in the values into the equations and perform the calculations.