A certain elevator car has mass 2200 kg and is lifted by cables driven by an electric motor. The efficiency of the lift system (motor, pulleys, cable, etc.) is 67.0%. As the elevator car moves at constant speed of 3.0 m/s it encounters 220N of friction coming from its tracks. Determine the electrical power requirement for this system as it lifts the car.
what is 1/.67 *( 2200*g+220)3 watts
Calculate the number of joules of kinetic energy a 1kg parrot has when it flies at 6 m/s
To determine the electrical power requirement for the elevator system, we need to consider the forces acting on the elevator car and the work done in lifting it.
First, let's determine the work done against friction. The frictional force opposing the motion of the elevator car is given as 220 N. The work done against friction can be calculated by multiplying the force of friction by the distance traveled:
Work against friction = Force of friction * Distance traveled
Since the elevator is moving at a constant speed of 3.0 m/s, we need to determine the time it takes to travel a certain distance. To do this, we divide the distance traveled by the velocity:
Time = Distance traveled / Velocity
Next, we need to determine the distance traveled in this time. The distance traveled can be calculated by multiplying the time by the velocity:
Distance traveled = Time * Velocity
Now that we have the distance traveled, we can calculate the work done against friction:
Work against friction = Force of friction * (Time * Velocity)
Next, let's determine the work done in lifting the elevator car. The work done in lifting an object can be calculated by multiplying the force applied to lift it by the distance it is lifted:
Work done in lifting = Force applied * Distance lifted
In this case, the force applied to lift the elevator car is equal to its weight, which can be calculated using the formula:
Force applied = Mass * gravity
Where the mass is given as 2200 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Now, we need to determine the distance lifted by the elevator car. Since it is moving at a constant speed of 3.0 m/s, we assume it is lifting vertically. Therefore, the distance lifted can be calculated by multiplying the time it takes to lift the car by the velocity:
Distance lifted = Time * Velocity
Finally, we can calculate the work done in lifting the elevator car:
Work done in lifting = Force applied * (Time * Velocity)
Next, we need to determine the electrical power requirement of the system. Power is the rate at which work is done, and it can be calculated by dividing the work done by the time taken:
Power = Work / Time
In this case, the total work done in the system is the sum of the work done against friction and the work done in lifting the car.
Finally, we multiply the calculated power by the efficiency of the system to account for any energy losses:
Electrical power requirement = Power * efficiency
Now that we have explained how to calculate the electrical power requirement for the elevator system, you can follow the steps outlined and substitute the given values into the equations to find the answer.