power in lifting= mgh/time=1200*9.8*30/90
power input= 5kW
efficiency fraction= lifting power/5kw
power input= 5kW
efficiency fraction= lifting power/5kw
To find the efficiency of the crane, we need to first calculate its output power and input power.
The work done by the crane to lift the load can be calculated using the formula:
Work (W) = Force (F) x Distance (d)
The force required to lift the load can be calculated using the formula:
Force (F) = Mass (m) x Acceleration due to gravity (g)
Since the load is being lifted vertically, the acceleration due to gravity (g) is approximately 9.8 m/s².
Force (F) = 1200 kg x 9.8 m/s²
Now, we can calculate the work done:
Work (W) = Force (F) x Distance (d) = (1200 kg x 9.8 m/s²) x (30 m)
The output power of the crane can be calculated using the formula:
Output Power = Work / Time
Output Power = (1200 kg x 9.8 m/s² x 30 m) / 90 s
To find the efficiency, we need to divide the output power by the input power.
Since the input power is given as 5.0 kW, we need to convert it to joules per second (Watts).
1 kW = 1000 Watts
Input Power = 5.0 kW x 1000 W/kW = 5000 W
Efficiency = (Output Power / Input Power) x 100
Now we can calculate the efficiency of the crane!
*Calculations ensue*
Drum roll, please...
After all the calculations, the efficiency of the crane is approximately [answer]. Keep in mind that this is just an estimate, and I apologize if my clown math went a little haywire!
The output power is the work done by the crane, which can be calculated using the formula:
Output Power = Work / Time
The work done by the crane is equal to the force applied (Weight of the load) multiplied by the distance over which the force is applied (height):
Work = Force x Distance
Work = (Weight of the load) x (Height)
The weight of the load can be calculated using the formula:
Weight = mass x gravity
Where mass is the mass of the load and gravity is the acceleration due to gravity.
Once we have the output power, we can then calculate the input power, which is the power input to the crane's motor.
The efficiency of the crane is then calculated as:
Efficiency = (Output Power / Input Power) x 100%
Now, let's calculate the efficiency of the crane step-by-step.
Given:
Power input to the motor (Input Power) = 5.0 kW
Mass of the load (m) = 1200 kg
Height (h) = 30 m
Time taken (t) = 90 s
First, we need to find the weight of the load:
Weight = mass x gravity
Where gravity is approximately 9.8 m/s^2.
Weight = 1200 kg x 9.8 m/s^2
Weight = 11760 N
Next, we calculate the work done by the crane:
Work = (Weight of the load) x (Height)
Work = 11760 N x 30 m
Work = 352800 J
Now, we can find the output power:
Output Power = Work / Time
Output Power = 352800 J / 90 s
Output Power = 3920 W
Finally, we calculate the efficiency:
Efficiency = (Output Power / Input Power) x 100%
Efficiency = (3920 W / 5000 W) x 100%
Efficiency = 78.4%
Therefore, the efficiency of the crane is 78.4%.
1. Calculate the output power:
The output power of the crane is the work done in lifting the load of bricks through a height. The work done can be calculated using the formula: work = force × distance.
The force can be calculated using the formula: force = mass × acceleration due to gravity.
Given:
Mass of the load (m) = 1200 kg
Height (h) = 30 m
Acceleration due to gravity (g) = 9.8 m/s²
Force (F) = m × g
Force = 1200 kg × 9.8 m/s²
Force = 11760 N
Work (W) = F × h
Work = 11760 N × 30 m
Work = 352800 J (joules)
The output power (Pout) can be calculated using the formula: power = work / time
Given:
Time (t) = 90 s
Output power (Pout) = work / time
Pout = 352800 J / 90 s
Pout = 3920 W (watts)
2. Calculate the input power:
The input power is given as 5.0 kW (kilowatts). We need to convert it to watts.
Input power (Pin) = 5.0 kW × 1000
Pin = 5000 W (watts)
3. Calculate the efficiency:
Efficiency is the ratio of output power to input power.
Efficiency = (output power / input power) × 100
Efficiency = (3920 W / 5000 W) × 100
Efficiency = 78.4%
Therefore, the efficiency of the crane is 78.4%.