A man loads 1000 sacks of flour into a truck in 30.0 minutes. Each sack has a mass of 20.0kg and the man must lift each sack 1.00m from a cart up onto the truck bed. how much power did the man develop?
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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, which is the product of force and distance. The force can be determined using Newton's second law:
Force = Mass * Acceleration
In this case, since the sacks are being lifted vertically, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, we have:
Force = Mass * Gravity
For each sack, the force can be calculated as:
Force = 20.0 kg * 9.8 m/s^2
Next, let's determine the total work done by calculating the work for each sack and multiplying it by the total number of sacks:
Work = Force * Distance * Total Number of Sacks
In this case, the distance is 1.00 m and the total number of sacks is 1000.
Finally, we can substitute the values into the formula to find the power:
Power = Work / Time
The time given in the question is 30.0 minutes, but to use the formula, we need to convert it to seconds by multiplying by 60:
Time = 30.0 minutes * 60 seconds/minute
Now, let's perform the calculations to find the power developed by the man:
Force = 20.0 kg * 9.8 m/s^2 = 196 N
Work = 196 N * 1.00 m * 1000 sacks = 196,000 J
Time = 30.0 minutes * 60 seconds/minute = 1800 s
Power = 196,000 J / 1800 s = 108.89 W
Therefore, the man developed approximately 108.89 watts of power while loading the sacks of flour onto the truck.