A elevator is rated at 25.0 kW. At what speed could the motor lift an 850 kg elevator with three passengers whose masses are 24.3 kg, 45.0 kg and 64.0 kg?
ideal power lifting elevator = weight * speed = m g v watts
m = 850 + 24.3 etc
g = 9.81 around here
so
25,000 =m g v
solve for v
To find the speed at which the motor could lift the elevator, we need to calculate the force required to lift the elevator and then use that force to determine the acceleration of the system.
Step 1: Calculate the total mass of the system.
Total mass of the system = Mass of the elevator + Sum of masses of the passengers
Total mass of the system = 850 kg + 24.3 kg + 45.0 kg + 64.0 kg
Total mass of the system = 983.3 kg
Step 2: Calculate the force required to lift the system.
Force = Mass × Acceleration (Newton's second law of motion)
Force = Total mass of the system × gravitational acceleration (9.8 m/s^2)
Force = 983.3 kg × 9.8 m/s^2
Force = 9630.34 N
Step 3: Calculate the power required by the motor.
Power (P) = Force × Velocity
We are given the power rating of the elevator motor as 25.0 kW. To convert this to watts, we multiply by 1000.
P = 25.0 kW × 1000
P = 25000 W
Step 4: Calculate the velocity.
Velocity = Power / Force
Velocity = 25000 W / 9630.34 N
Velocity ≈ 2.60 m/s
Therefore, the elevator motor could lift the 850 kg elevator with the three passengers at a speed of approximately 2.60 m/s.
To find the speed at which the elevator motor can lift the elevator and passengers, we can use the principle of work and power. Power is defined as the rate at which work is done, and work is given by the formula:
Work = Force x Distance
In this case, the force is the weight of the elevator and passengers, and the distance is the height the elevator needs to travel. The weight is given by the formula:
Weight = Mass x Gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
First, let's calculate the total weight of the elevator and passengers:
Total weight = Mass of elevator + Mass of passengers
Total weight = 850 kg + (24.3 kg + 45.0 kg + 64.0 kg)
Total weight = 983.3 kg
Next, let's calculate the work done by the elevator motor. The work done is equal to the weight multiplied by the height the elevator needs to travel. However, since we don't have the height, we can rearrange the power formula to solve for height:
Power = Work / Time
Work = Power x Time
Since the elevator is rated at 25.0 kW, we need to convert the power to Watts:
Power = 25.0 kW = 25,000 W
Assuming the elevator motor can lift the elevator and passengers in 5 seconds (Time = 5 s), we can now calculate the work done:
Work = Power x Time
Work = 25,000 W x 5 s
Work = 125,000 J (Joules)
Now that we have the work done, we can calculate the height using the formula:
Work = Force x Distance
125,000 J = Total weight x Distance
Distance = 125,000 J / Total weight
Distance = 125,000 J / 983.3 kg
Distance ≈ 127.15 m
Finally, we can calculate the speed using the formula:
Speed = Distance / Time
Speed = 127.15 m / 5 s
Speed ≈ 25.43 m/s
Therefore, the motor can lift the elevator and passengers at a speed of approximately 25.43 m/s.