a hoist powered by a 10 kw motor is used to raise a bucket filled with 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
To find the time needed to raise the bucket filled with concrete to a height of 80 m using a hoist powered by a 10 kW motor with an 80% efficiency, we can follow these steps:
Step 1: Calculate the power output of the hoist.
Given that the hoist has an efficiency of 80% and a power input of 10 kW, we can find the power output using the formula:
Power output = Efficiency x Power input
Substituting the given values, we have:
Power output = 0.80 x 10 kW
Power output = 8 kW
Therefore, the power output of the hoist is 8 kW.
Step 2: Calculate the work done in raising the bucket.
The work done can be calculated using the formula:
Work = Force x Distance
The force required to raise the bucket can be found using Newton's second law of motion, which states that Force = Mass x Acceleration. Since the bucket is not accelerating (moving at a constant speed), the force required is equal to the weight of the bucket.
Weight = Mass x Gravity
Substituting the values, we have:
Weight = 500 kg x 9.8 m/s^2
Weight = 4900 N
Therefore, the force required to raise the bucket is 4900 N.
The work done can now be calculated:
Work = Force x Distance
Work = 4900 N x 80 m
Work = 392,000 J
Step 3: Calculate the time needed.
Since power is the rate at which work is done, we can calculate the time needed using the formula:
Time = Work / Power output
Substituting the values, we have:
Time = 392,000 J / 8,000 W
Time = 49 seconds
Therefore, the time needed to raise the bucket filled with concrete to a height of 80 m is 49 seconds.