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 period when it accelerates, we can use the formula:
Power = (Force x Distance) / Time
First, we need to find the force exerted by the elevator motor during the acceleration phase. We can do this by using Newton's second law of motion:
Force = Mass x Acceleration
Given:
Mass (m) = 690 kg
Time (t) = 2.56 s
Cruising speed (v) = 1.84 m/s
Acceleration (a) can be found using the equation:
v = u + at
where u is the initial velocity.
Since the elevator starts from rest, u = 0 m/s:
1.84 m/s = 0 m/s + a(2.56 s)
a = 1.84 m/s / 2.56 s
a ≈ 0.72 m/s^2
Now we can calculate the force:
Force = Mass x Acceleration
= 690 kg x 0.72 m/s^2
= 496.8 N
Next, we need to find the distance traveled by the elevator during the acceleration phase. We can use the equation:
Distance = (Initial velocity x Time) + (0.5 x Acceleration x Time^2)
Again, since the elevator starts from rest, the initial velocity is 0 m/s:
Distance = 0.5 x 0 x (2.56 s)^2 + 0.5 x 0.72 m/s^2 x (2.56 s)^2
= 0 + 0.5 x 0.72 m/s^2 x (2.56 s)^2
= 2.1 m
Now we can calculate the average power:
Power = (Force x Distance) / Time
= (496.8 N x 2.1 m) / 2.56 s
= 405.35 W
Therefore, the average power of the elevator motor during the period of acceleration is approximately 405.35 watts.
To find the power of the elevator motor during the upward cruise with constant speed, we need to use the formula:
Power = Force x Velocity
Since the elevator is in a constant speed cruising phase, the force required to maintain the speed is zero:
Power = 0 x 1.84 m/s
= 0 W
Therefore, the power of the elevator motor during the upward cruise with constant speed is zero.
To find the average power of the elevator motor during the period of constant acceleration, we can use the formula:
Power = (Force * Distance) / Time
First, let's find the force acting on the elevator. We know that force is equal to mass times acceleration:
Force = mass * acceleration
Given:
Mass (m) = 690 kg
Acceleration (a) = (final velocity - initial velocity) / time = (1.84 m/s - 0) / 2.56 s
Now we can calculate the force:
Force = 690 kg * ((1.84 m/s - 0) / 2.56 s)
Next, we need to calculate the distance traveled during the constant acceleration phase. We can use the formula:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
We're given that the elevator starts from rest, so the initial velocity (v0) is 0. Plugging in the values:
Distance = (0 * 2.56 s) + (0.5 * ((1.84 m/s - 0) / 2.56 s) * (2.56 s)^2)
Now, we have all the values needed to calculate the average power:
Power = (Force * Distance) / Time
Power = (690 kg * ((1.84 m/s - 0) / 2.56 s)) * (0 * 2.56 s) + (0.5 * ((1.84 m/s - 0) / 2.56 s) * (2.56 s)^2)) / 2.56 s
After calculating the equation above, we can determine the average power of the elevator motor during the period of constant acceleration.
To find the power of the elevator motor during the upward cruise with constant speed, we can use the formula:
Power = Force * Velocity
We have already calculated the force acting on the elevator during the constant acceleration phase. The velocity during the cruise phase is 1.84 m/s. Plug in the values:
Power = (690 kg * ((1.84 m/s - 0) / 2.56 s)) * 1.84 m/s
After simplification, we can find the power of the elevator motor during the upward cruise with constant speed.