A 685 kg elevator starts from rest and moves upward for 2.80 s with constant acceleration until it reaches its cruising speed, 1.71 m/s.
(a) What is the average power of the elevator motor during this period?
(b) What is the average power during an upward cruise with constant speed?
To find the average power of the elevator motor during this period, we need to use the formula for power:
Power = Force x Velocity
First, let's find the force exerted by the elevator motor during the period of acceleration.
Using Newton's second law, which states that Force (F) is equal to mass (m) multiplied by acceleration (a):
F = m x a
Given:
Mass (m) = 685 kg
The elevator starts from rest and reaches a cruising speed, which means it undergoes constant acceleration. However, we don't know the acceleration rate.
To find the acceleration, we can use the following kinematic equation:
V = u + at
Where:
V is the final velocity (1.71 m/s),
u is the initial velocity (0 m/s since the elevator starts from rest),
a is the acceleration, and
t is the time taken (2.80 s).
Rearranging the equation to isolate the acceleration (a):
a = (V - u) / t
Applying the values we have:
a = (1.71 m/s - 0 m/s) / 2.80 s
a = 1.71 m/s / 2.80 s
a = 0.6107 m/s²
Now that we have the acceleration, we can calculate the force exerted by the elevator motor:
F = m x a
F = 685 kg x 0.6107 m/s²
F = 418.3935 N
Next, we need to calculate the average power during this period using the formula:
Power = Force x Velocity
Given:
Velocity (v) = 1.71 m/s
Power = F x v
Power = 418.3935 N x 1.71 m/s
Power = 715.4819 W
Therefore, the average power of the elevator motor during this period is approximately 715.48 W.
Now, let's move on to the second part of the question:
To find the average power during an upward cruise with constant speed, we need to know the force exerted by the elevator. Since the elevator is moving at a constant speed, the net force acting on it is zero. This means that the motor doesn't have to exert any force during this period.
When the net force is zero, the power is also zero. This is because power is the rate at which work is done, and if no work is being done (no force applied), then the power is zero.
Therefore, the average power during an upward cruise with constant speed is zero.