A hoist powered by a 10 kw motor is used to raise a bucket filled wirh concrete and having total mass of 500 kg to height of 80 m. if the efficiency of the hoist is 80 percent, find Time needed
m g h = 500 * 9.8 * 80 Joules
80% of 10 kw is 8 kJ per second
looks like about a minute
A hoist powered by a 15-kW motor is used to raise a bucket filled with concrete and having a total mass of 500 kg to a height of 60 m
To find the time needed to raise the bucket, we first need to calculate the work done by the hoist. Work done is equal to the product of force and distance moved.
The force needed to lift the bucket can be calculated using the equation:
Force = mass x acceleration due to gravity
Given that the mass of the bucket is 500 kg and acceleration due to gravity is 9.8 m/s^2, we can calculate the force:
Force = 500 kg x 9.8 m/s^2 = 4900 N
The work done by the hoist can be calculated as:
Work = Force x distance
Given that the distance is 80 m, we can calculate the work done:
Work = 4900 N x 80 m = 392,000 Nm or 392 kJ
Now, we need to calculate the input power of the hoist. The power is calculated as the work done per unit time:
Power = Work / Time
Given that the power of the motor is 10 kW and the efficiency is 80%, we can calculate the input power to the hoist:
Input Power = Motor Power / Efficiency
Input Power = 10 kW / 0.80 = 12.5 kW
Now, we can rearrange the power equation to find the time needed:
Time = Work / Power
Time = 392 kJ / 12.5 kW = 31.36 seconds
Therefore, the time needed to raise the bucket filled with concrete to a height of 80 m using the hoist is approximately 31.36 seconds.
To find the time needed to raise the bucket, we can use the equation for power:
Power = Work/Time
Since we are given the power and efficiency, we can calculate the work done by the hoist.
Efficiency is defined as the ratio of useful work output to the total work input:
Efficiency = (Useful Work Output / Total Work Input) * 100
In this case, the useful work output is the work done by the hoist to raise the bucket, and the total work input is the power supplied by the motor.
Useful Work Output = Work done by the hoist
Total Work Input = Power supplied by the motor
Efficiency = (Work done by the hoist / Power supplied by the motor) * 100
Since the efficiency is given as 80%, we can write this equation as:
80 = (Work done by the hoist / Power supplied by the motor) * 100
Solving for Work done by the hoist:
Work done by the hoist = (80/100) * Power supplied by the motor
Given that the power supplied by the motor is 10 kW, we can substitute it into the equation:
Work done by the hoist = (80/100) * 10 kW
= 8 kW
Now, we can use the work done by the hoist to find the time needed to raise the bucket.
Work done = Force * Distance
In this case, the Force is the weight of the bucket, which can be calculated as the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
Weight of the bucket = Mass of the bucket * Acceleration due to gravity
= 500 kg * 9.8 m/s^2
= 4900 N
Now we can substitute the values into the equation:
Work done by the hoist = Force * Distance
8 kW = 4900 N * 80 m
To find the time needed, we need to rearrange the equation:
Time = Work done / Power
Substituting the values:
Time = (Work done by the hoist) / (Power supplied by the motor)
= 8 kW / 10 kW
= 0.8 hour
Therefore, the time needed to raise the bucket is 0.8 hour, or equivalently, 48 minutes.