Ten boxes, each 16.0 cm high and weighing 250 N, initially are all side by side on the floor. The boxes are lifted and placed in a vertical stack 1.60 m high in a time interval of 7.00 s. Compute the power necessary to stack the boxes.
To compute the power necessary to stack the boxes, we will use the formula:
Power = Work/Time
First, let's determine the work done in lifting the boxes.
Work = Force x Distance
The force required to lift one box is its weight, which is given as 250 N.
To calculate the distance, we need to determine how far the boxes were lifted. From the problem statement, the initial height of each box is 16.0 cm, and the final height of the stack is 1.60 m.
To convert the height to meters:
Initial height = 16.0 cm = 0.16 m
Final height = 1.60 m
The distance the boxes were lifted is the difference in height:
Distance = Final height - Initial height
Distance = 1.60 m - 0.16 m = 1.44 m
Now, we can calculate the work done:
Work = Force x Distance
Work = 250 N x 1.44 m = 360 J
Next, we need to calculate the time interval given, which is 7.00 s.
Finally, we can calculate the power using the formula:
Power = Work/Time
Power = 360 J / 7.00 s ≈ 51.43 W
Therefore, the power necessary to stack the boxes is approximately 51.43 Watts.