Question

a solid cube is submerged under oil in a vat and is tied to the bottom with a string. what is the magnitude of the tension in the string if the side of the cube is 14 cm and the density of oil is 110 kg/m³ greater than the cube's density?

Answer 1

The magnitude of the tension in the string holding a submerged cube in oil can be calculated using the side length of the cube and the difference in density between the oil and the cube, applying the principles of buoyancy and Archimedes' principle.

Step-by-step explanation:

The student has asked how to calculate the magnitude of the tension in the string that is holding a solid cube submerged in oil. Given that the side of the cube is 14 cm and the density of the oil is 110 kg/m³ greater than the cube, we will need to apply concepts from buoyancy and Archimedes' principle to deduce the tension in the string.

First, we calculate the volume of the cube, which can be found using the cube's side length (14 cm or 0.14 m), and then the weight of the cube using its volume and density. Next, we find the buoyant force acting on the cube by the oil, which depends on the volume of displaced oil and the difference in density between the oil and the cube. The tension in the string will be the difference between the weight of the cube and the buoyant force.

To calculate these values, we can use the following formulas: Volume of cube = side³, Weight of cube = volume × (density of cube × gravity), and Buoyant force = volume × (density of oil × gravity). Finally, Tension = weight - buoyant force.