Final answer:
To determine how far the empty jar will sink into water, one must calculate the volume of the glass shell, determine the weight of the jar, and apply Archimedes' principle to equate the jar's weight with the buoyant force of the water displaced by the jar.
Step-by-step explanation:
To find the distance an empty jar will sink into the water, we must first calculate the volume of the glass shell of the jar. The jar's inside radius is 3.00 inches, and it has a wall thickness of 3/16 inches, so the outer radius is 3.00 inches + 3/16 inches. To convert the radius to feet, we use the conversion: 1 inch = 1/12 foot. We calculate the volume of the jar by considering it as the difference between two cylinders (the larger cylinder representing the outer dimensions and the smaller cylinder representing the inner void).
The volume (V) of a cylinder is given by V = π × r² × h, where r is the radius, and h is the height. First, we need to find the volume of the outer cylinder (V_outer) with the outer radius and the volume of the inner cylinder (V_inner) with the inside radius, both with the same height. Then, the glass shell's volume (V_glass) is V_outer - V_inner. Finally, we can find out how far the jar will sink into the water by equating the weight of the jar to the weight of the displaced water, as per Archimedes' principle.
The weight of the jar is found by multiplying the volume of the glass (V_glass) by the density of the glass and converting the weight to force (in pounds-force) using the acceleration due to gravity. The buoyant force of the water is equal to the weight of the displaced water, which can be found by multiplying the density of water by the volume of the submerged part of the jar and again converting this to force.
By setting the weight of the jar equal to the buoyant force, we can find the volume of the submerged part of the jar. Assuming the jar does not tip and remains upright, this volume will be the same shape as the jar but with a different height, h_submerged, which can be calculated using the cylinder volume formula. From there, we can obtain the height submerged in feet and convert it to inches for the result.