A man loads 1,000 sacks of flour into a truck in 30.0 minuets.Each sack has a mass of 20.0 kg and the man must lift each sack 1.00 m from a cart up onto the truck bed. How much power did the man develop ?
To calculate the power developed by the man, we need to use the formula:
Power = Work / Time
First, let's calculate the work done by the man. Work is given by the formula:
Work = Force x Distance
In this case, the force is equal to the weight of each sack, and the distance is the height the man lifted each sack. The weight of each sack can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
Given that each sack has a mass of 20.0 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of each sack:
Weight = 20.0 kg x 9.8 m/s² = 196.0 N
The distance lifted is 1.00 m, and the man lifted 1,000 sacks. So, the total work done by the man is:
Work = Force x Distance = (196.0 N) x (1.00 m) x (1000 sacks) = 196,000 J
Now, we can calculate the power developed by the man using the work done and the time taken. The time taken is given as 30.0 minutes, but we need to convert it to seconds:
Time = 30.0 minutes x 60 seconds/minute = 1800 seconds
Finally, we can calculate the power:
Power = Work / Time = 196,000 J / 1800 s ≈ 108.9 Watts
Therefore, the man developed approximately 108.9 Watts of power.