A crane accidently drops a box full of material into a freshwater pool measuring 20 feet long, 10 feet wide, and 6 feet deep before the box is dropped causing the water level to rise to 6.05 feet after the box is dropped. The box is 10x8x12 inches and the material inside weighs 2.4 lbs/in3. Water weighs 8.3 lbs/gallon. Will the object sink or float?
To determine whether the object will sink or float, we need to compare the weight of the object to the weight of the water it displaces.
First, let's calculate the weight of the water displaced by the box when it is dropped into the pool.
The volume of the box can be calculated by multiplying its length, width, and height:
Volume = 10 inches x 8 inches x 12 inches = 960 cubic inches.
To convert the volume from cubic inches to cubic feet, we divide by 12x12x12:
Volume = 960 cubic inches / (12 inches/foot)^3 = 0.5556 cubic feet (rounded to four decimal places).
The weight of the water displaced can be calculated by multiplying the volume by the density of water (8.3 lbs/gallon):
Weight of water displaced = 0.5556 cubic feet x 8.3 lbs/gallon = 4.60548 lbs (rounded to five decimal places).
Now, let's calculate the weight of the box:
The volume of the box is 10x8x12 cubic inches, which is equal to 10/12 x 8/12 x 12/12 cubic feet (since there are 12 inches in a foot):
Volume = (10/12) feet x (8/12) feet x (12/12) feet = 0.5556 cubic feet (rounded to four decimal places).
The weight of the box can be calculated by multiplying the volume by the density of the material (2.4 lbs/in3):
Weight of the box = 0.5556 cubic feet x 2.4 lbs/in3 = 1.3334 lbs (rounded to four decimal places).
Comparing the weight of the water displaced (4.60548 lbs) to the weight of the box (1.3334 lbs), we can see that the weight of the displaced water is greater than the weight of the box. Therefore, the object will float in the pool.