A 200-pound boy lifts a 40-kilogram box off of the floor 1.3 meters in 0.7 seconds. His brother lifts a 48-kilogram box off the floor 0.9 meters in 0.6 seconds. Which boy is more powerful? Explain.
Wb = m*g = 40kg * 9.8N/kg = 392 N, = Wt.
of the box.
P1 = F*d/t = 392 * 1.3/0.7 = 728 J/s =
728 Watts.
Wb = 48kg * 9.8N/kg = 470.4 N.
P2=470.4 * 0.9/0.6=706. J/s=706Watts.
The 1st boy is more powerful.
To determine which boy is more powerful, we need to compare the work done by each boy. Work is defined as the product of force and distance. In this case, the force is the weight lifted and the distance is the height the box is raised.
First, let's convert the measurements to a consistent unit system. We'll convert pounds to kilograms and feet to meters.
The weight of the first boy is given in pounds, so let's convert that to kilograms.
1 pound is approximately 0.4536 kilograms.
So, the weight of the first boy is 200 * 0.4536 = 90.72 kilograms.
Now, let's calculate the work done by the first boy.
Work1 = Force1 * Distance1
= 90.72 kg * 1.3 meters
= 117.936 kilogram-meters (kg⋅m)
Similarly, let's convert the weight of the second boy to kilograms.
The weight of the second boy is already given in kilograms (48 kilograms).
Now, calculate the work done by the second boy.
Work2 = Force2 * Distance2
= 48 kg * 0.9 meters
= 43.2 kilogram-meters (kg⋅m)
Now, we can compare the work done by each boy. The larger the work done, the more powerful the boy is.
Comparing the calculated values:
Work1 = 117.936 kg⋅m
Work2 = 43.2 kg⋅m
From the comparison, we can conclude that the first boy is more powerful, as he exerted more work in lifting the box compared to the second boy.