fully loaded, slow-moving freight elevator has a cab with a total mass of 1250 kg, which is required to travel upward 58 m in 3.4 min, starting and ending at rest. The elevator's counterweight has a mass of only 1005 kg, and so the elevator motor must help. What average power is required of the force the motor exerts on the cab via the cable?
________W
The lifting force is (1250-1005)g
or force=245g
power=work/time=245*58/(3.4*60)
force of gravity on elevator is
1250 kg * 9.8= 12250 N
Force of counter weight is
1005 kg * 9.8= 9849 N
12250 N - 9849 N = 2761 N Total
P = (F*d)/T
To find the average power required of the force the motor exerts on the cab via the cable, we can use the formula:
Average Power = Work / Time
First, let's find the work done by the force to lift the cab.
Work = Force x Distance
The force required is equal to the weight of the cab and the counterweight combined. The weight is calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s^2).
Weight of the cab = mass of the cab x acceleration due to gravity = 1250 kg x 9.8 m/s^2
Weight of the counterweight = mass of the counterweight x acceleration due to gravity = 1005 kg x 9.8 m/s^2
Total weight = Weight of the cab + Weight of the counterweight
Next, we can calculate the distance traveled by the cab.
Distance = 58 m
Now, we can calculate the work done.
Work = Total weight x Distance
Finally, we can calculate the average power.
Average Power = Work / Time
Given:
- Distance = 58 m
- Time = 3.4 min = 3.4 x 60 s
Let's plug in the values and calculate the average power.
To find the average power required of the force the motor exerts on the cab via the cable, we need to use the formula:
Power = Work / Time
First, let's calculate the work done by the force. The work done by a force can be found using the formula:
Work = Force x Distance
In this case, the force is the net force acting on the cab. The net force is equal to the difference between the force exerted by the motor and the force exerted by the weight of the elevator and the counterweight.
To find the force exerted by the weight, we can use the formula:
Force = Mass x Gravity
The mass of the cab is given as 1250 kg, and the mass of the counterweight is given as 1005 kg. The total mass of the system is the sum of the cab mass and the counterweight mass.
The acceleration due to gravity (g) is a constant value of approximately 9.8 m/s^2.
Next, we need to calculate the distance traveled by the cab. The distance is given as 58 m.
Finally, we can substitute the calculated values into the formula for work to find the work done by the force.
Once we have the work done by the force, we can divide it by the given time of 3.4 minutes (convert to seconds) to get the average power required.
Let's calculate the average power step by step:
Step 1: Calculate the total mass of the system:
Total mass = mass of the cab + mass of the counterweight
Total mass = 1250 kg + 1005 kg
Total mass = 2255 kg
Step 2: Calculate the force exerted by the weight:
Force = mass x gravity
Force = 2255 kg x 9.8 m/s^2
Force ≈ 22,129 N
Step 3: Calculate the work done by the force:
Work = force x distance
Work = 22,129 N x 58 m
Work ≈ 1,281,682 J
Step 4: Convert the given time from minutes to seconds:
Time = 3.4 min x 60 s/min
Time = 204 s
Step 5: Calculate the average power:
Power = Work / Time
Power = 1,281,682 J / 204 s
Power ≈ 6291 W
Therefore, the average power required of the force the motor exerts on the cab via the cable is approximately 6291 Watts.