Final answer:
The upthrust acting on the submerged cube is calculated using Archimedes' principle and equals 62784 N. The tension in the cable is found by subtracting the upthrust from the weight of the block, resulting in a tension of 15696 N.
Step-by-step explanation:
To answer the student's question regarding the cube of side 2.0m and mass 4800kg attached to the base of a tank containing paraffin of density 800kg/m³, we will first need to calculate the upthrust (buoyant force) acting on the block, and then determine the tension in the cable.
Calculating Upthrust
To find the upthrust on the block submerged in paraffin, we can use Archimedes' principle which states that the upthrust on a submerged object is equal to the weight of the fluid displaced by the object. The upthrust (U) can be calculated as:
U = Volume of Block × Density of Paraffin × Gravitational Acceleration
The volume of the cube is given by the formula V = s³, where s is the length of the side of the cube. Hence, V = 2.0m × 2.0m × 2.0m = 8.0m³.
Now, we can substitute the known values: U = 8.0 m³ × 800 kg/m³ × 9.81 m/s² = 62784 N.
Calculating Cable Tension
The tension in the cable (T) will be the difference between the weight of the block and the upthrust. The weight (W) of the block is calculated by W = Mass of Block × Gravitational Acceleration, which gives us W = 4800kg × 9.81 m/s² = 47088 N.
Thus, the tension in the cable is T = W - U = 47088 N - 62784 N = -15696 N. However, since tension cannot be negative, we take the absolute value, giving us T = 15696 N.