Bowling balls can be made from a variety of substances and are required to have a circumference of roughly 27.2 inches. The cons
truction of the ball typically consists of a high density core surrounded by a lower density shell. Suppose a bowling ball floats in water with half of its volume submerged. If the specific gravity of the shell is 0.350 and the specific gravity of the core is 0.920, calculate the thickness of the shell.
1 answer:
Answer:
The bowlling shell's thickness is 2.7"
Explanation:
The geometry of the problem is based in the differences between the volumes in a small sphere and a spherical shell, both objects compose the total volume of the bowling ball.
The equivalence in the total ball height and the equivalent height in the fluid (in this case water displacement of half ball volume) is used for calculating the forces state that allows the static balance of the ball and the flotation force from the fluid (Archimedes principle).
In the image is showed the formulation.
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A) Net force in component form:
B) Magnitude of the net force: 316.2, direction:
Explanation:
A)
The three forces given in this problem are:
The three forces are given in component form, where the components with unit vector i is the component along the x-direction, while the components with unit vector j is the component along the y-direction.
In order to find the net force in component form, we just need to add the components of the three forces along each direction. Therefore:
- Along the x-direction:
- Along the y-direction:
So, the net force in component form is
B)
The magnitude of a vector F is given by Pythagorean's theorem:
where in this problem,
is the x-component
is the y-component
Substituting,
The direction instead is given by
where the negative sign means the direction is below the positive x-axis.
Learn more about vector addition:
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