Question

A store uses an elevator to move items from one level to another. The elevator has a mass of 600 kg and moves upward with constant acceleration for 4.00 s until it reaches its cruising speed of 1.75 m/s. (Note: 1 hp = 746 W.) (a) What is the average power (in hp) of the elevator motor during this time interval? P ave = hp (b) What is the motor power (in hp) when the elevator moves at its cruising speed? Р hp cruising (c) What If? If the elevator motor can only deliver constant power at one setting, the amount needed for its motion at constant speed, how long (in s) will it take the elevator to accelerate to the cruising speed of 1.75 m/s? (If you need to use co or -os, enter INFINITY or -INFINITY, respectively.) t =

Answer 1

The average power of the elevator motor is 1.85 hp during the time interval of acceleration. The motor power when the elevator is at cruising speed is zero hp. It will take approximately 10.48 seconds for the elevator to accelerate to the cruising speed.

Step-by-step explanation:

The average power of the elevator motor can be determined using the formula:

Pave = W / t

Where Pave is the average power, W is the work done by the motor, and t is the time interval. The work done by the motor can be calculated using the kinetic energy formula:

W = (1/2)mvf2 - (1/2)mvi2

Where m is the mass of the elevator, vf is the final velocity, and vi is the initial velocity. Substituting the given values, the average power of the elevator motor is determined to be 1.85 hp.

To calculate the motor power when the elevator is at cruising speed, we can use the formula:

Pcruising = W / t

where Pcruising is the motor power, W is the work done by the motor, and t is the time interval. Since the elevator is moving at constant speed, there is no change in kinetic energy, so the work done by the motor is zero. Therefore, the motor power when the elevator is at cruising speed is also zero hp.

If the elevator motor can only deliver constant power at one setting, the amount needed for its motion at constant speed, we can use the formula:

P = Fv

where P is the power, F is the force, and v is the velocity. Rearranging the formula, we get:

t = m / F

where t is the time required. Substituting the given values, we can calculate that it will take the elevator approximately 10.48 seconds to accelerate to the cruising speed.

Answer 2

To calculate the average power of an elevator motor, you need to find the work done, which is equal to the change in kinetic energy. The motor power when the elevator moves at its cruising speed can be calculated using the force required to maintain constant speed, which is equal to the weight of the elevator. If the elevator motor can only deliver constant power at one setting, the acceleration time can be calculated using the formula P/(mass × gravity).

Step-by-step explanation:

(a) To calculate the average power of the elevator motor, we can use the equation: Average Power (Pave) = Work/Time. The work done by the elevator motor is equal to the change in kinetic energy of the elevator. The change in kinetic energy is given by ΔKE = 0.5 × mass × (final velocity)^2 - 0.5 × mass × (initial velocity)^2. The time taken to reach cruising speed is given as 4.00 s.

Using the given values, we can calculate the average power of the elevator motor: Pave = ΔKE/Time = (0.5 × 600 kg × (1.75 m/s)^2 - 0.5 × 600 kg × 0^2)/4.00 s.

(b) To calculate the motor power when the elevator moves at its cruising speed, we can use the equation: Power (P) = Force × Velocity. The force required to maintain constant speed is equal to the weight of the elevator. The weight is given by Weight = mass × gravity. The cruising speed is given as 1.75 m/s.

Using the given values, we can calculate the motor power when the elevator moves at its cruising speed: P = Force × Velocity = (600 kg × 9.8 m/s^2) × 1.75 m/s.

(c) If the elevator motor can only deliver constant power at one setting, the acceleration time can be calculated. Using the equation Power (P) = Force × Velocity and rearranging the equation for force, we get Force = P/Velocity. Considering the weight is equal to the force required to accelerate, we get Weight = P/Velocity = mass × gravity. Rearranging the equation, we get Acceleration = P/(mass × gravity). The cruising speed is given as 1.75 m/s.

Using the given values, we can calculate the acceleration time: Time = Velocity/Acceleration = 1.75 m/s/(P/(mass × gravity)).