A 645-kg elevator starts from rest. It moves upward for t = 3.13 s with a constant acceleration until it reaches its constant cruising speed of v = 1.26 m/s. It moved 2.75m during that time.
a) What is the average power (W)is delivered by the motor during the initial acceleration of the eleator during the first 3.13s?
b) How much power by the elevator motor while the elevator moves upward now at cruising speed?
Fe = mg = 645 kg * 9.8 N/kg = 6321 N. =
Force of elevator.
a. P = F * d/t = 6321 * 2.75 = 17382.75J
That is the increase in potential, now we must add the increase in kinetic energy, which is:
Ws = 1/2 m(Vf)^2 - 1/2 m(Vi)^2
Ws = 1/2 645kg(1.26m/s)^2 - 0
Ws = 512.001J
adding the two together we get:
512.001J + 17382.75J = 17894.751J
17894.751/3.13 = 5717.173 J/s. = 5717 W.
b. P = F*V = 6321 * 1.26 = 7965 J/s. =
7965 W.
To find the average power delivered by the motor during the initial acceleration of the elevator and the power while the elevator moves upward at cruising speed, we need to use the following formulas:
a) Average power (P) = Work done (W) / Time taken (Δt)
b) Power (P) = Force (F) × Velocity (v)
a) To find the average power during the initial acceleration of the elevator, we need to calculate the work done during that time period. The formula for work is:
Work (W) = Force (F) × Distance (d)
First, let's find the force (F). We can use Newton's second law of motion:
F = mass (m) × acceleration (a)
Given:
Mass (m) = 645 kg (mass of the elevator)
Time (Δt) = 3.13 s (time during the initial acceleration)
Distance (d) = 2.75 m (distance moved during the initial acceleration)
Velocity (v) = 1.26 m/s (constant cruising speed)
To find the acceleration (a), we can use the formula:
a = Δv / Δt
Where Δv is the change in velocity during the initial acceleration. As the elevator starts from rest (v = 0) and reaches a constant cruising speed (v = 1.26 m/s), the change in velocity will be:
Δv = v - 0 = 1.26 m/s - 0 = 1.26 m/s
Now we can calculate the acceleration:
a = Δv / Δt = 1.26 m/s / 3.13 s = 0.4025 m/s^2
Next, let's calculate the force:
F = m × a = 645 kg × 0.4025 m/s^2 = 259.6125 N
Now we can calculate the work done:
W = F × d = 259.6125 N × 2.75 m = 713.18375 J
Finally, we can calculate the average power:
P = W / Δt = 713.18375 J / 3.13 s = 227.733 W
Therefore, the average power delivered by the motor during the initial acceleration of the elevator is 227.733 W.
b) To find the power while the elevator moves upward at cruising speed, we need to calculate the force required when moving at that constant speed.
The force (F) required to maintain a constant velocity can be found using the formula:
F = m × a
Where m is the mass of the elevator and a is the acceleration (which is zero because there is no change in velocity).
Given:
Mass (m) = 645 kg
Now we can calculate the force:
F = m × a = 645 kg × 0 m/s^2 = 0 N
Finally, we can calculate the power:
P = F × v = 0 N × 1.26 m/s = 0 W
Therefore, the power delivered by the elevator motor while the elevator moves upward at cruising speed is 0 W, as no work is being done to maintain a constant velocity.
Fe = mg = 645 kg * 9.8 N/kg = 6321 N. =
Force of elevator.
a. P = F * d/t = 6321 * 2.75/3.13 = 5554 J/s. = 5554 W.
b. P = F*V = 6321 * 1.26 = 7965 J/s. =
7965 W.