A 690 kg elevator starts from rest. It moves upward for 2.56 s with constant acceleration until it reaches its cruising speed, 1.84 m/s. What is the average power of the elevator motor during this period?
What is the power of the elevator motor during an upward cruise with constant speed?
To find the average power of the elevator motor during the acceleration period, we need to calculate the work done by the motor first.
The work done on an object is given by the formula: Work = Force x Distance
In this case, the force acting on the elevator is the force of gravity and the force exerted by the motor. The net force is calculated by subtracting the force of gravity from the force exerted by the motor.
The force of gravity acting on the elevator is given by the formula: Force_gravity = mass x gravity
where mass is the mass of the elevator (690 kg) and gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
The net force is calculated by subtracting the force of gravity from the force exerted by the motor:
Force_net = mass x acceleration
where acceleration is the acceleration of the elevator during the period (we need to find this value).
Since the elevator starts from rest, we can use the equation of motion to find the acceleration:
Vf = Vi + a*t,
where Vf is the final velocity (1.84 m/s), Vi is the initial velocity (0 m/s), a is the acceleration, and t is the time interval (2.56 s).
Plugging in the values, we get:
1.84 m/s = 0 m/s + a * 2.56 s
Solving for a, we find:
a = (1.84 m/s) / (2.56 s)
Now that we have the acceleration, we can calculate the net force:
Force_net = mass x acceleration
Force_net = (690 kg) * (1.84 m/s) / (2.56 s)
Once we have the net force, we can calculate the work done by the motor:
Work_motor = Force_net x Distance
To find the distance traveled during the acceleration period, we can use the equation of motion:
Distance = Vi * t + 1/2 * a * t^2
Since the initial velocity is 0 and the time interval is 2.56 s, the equation simplifies to:
Distance = 1/2 * a * t^2
Plugging in the values, we get:
Distance = 1/2 * ((1.84 m/s) / (2.56 s)) * (2.56 s)^2
Finally, we can calculate the work done by the motor:
Work_motor = Force_net x Distance
The average power is given by the formula:
Average Power = Work_motor / time interval
Plugging in the values, we can find the average power of the elevator motor during the acceleration period.
To find the power of the elevator motor during the upward cruise with constant speed, we need to consider that the cruising speed means that the elevator is moving with a constant velocity. When the velocity is constant, the net force is zero since there is no acceleration. Therefore, the power of the elevator motor during the upward cruise with constant speed is zero.
Please note that the calculations provided are based on the given information and assumptions about the system.