Tension Force on The Cable

Question

I've been given a problem. I need to work out the tension force on the cable. Imagine there's a cylinder and it has a height of 0.51m and diameter of 7.9m and a density of $550kg/m^3$ Also, the cylinder is submerged 0.8 in water. Also the density of the water is $5000kg/m^3$

Answer 1

Since you've shown some work, I'll try to help despite the fact that this question is better suited for a physics site.

Consider the forces acting on the cylinder. The three key forces that need to balance for its equilibrium are: the tension force of the cable pulling on the cylinder, the weight of the cylinder (gravitational pull on the cylinder by the Earth) and the buoyant force of the water on the cylinder (which is the unbalanced force due to the pressure acting on the base of the cylinder).

Note the directions: weight is downward, buoyant force is upward and the tension is downward too (the cable has to pull down on the cylinder as the cylinder pulls up on the cable - this is an action-reaction pair (Newton's third law) and it's the only way the cable will remain taut).

Setting it all up:

Weight $W = mg = \rho_{cyl}\pi r^2 h g$

Buoyant force $F_b = \rho_{wat}\cdot g \cdot (0.8h) \cdot \pi r^2 = 0.8\rho_{wat}\pi r^2 h g$

So $T + W = F_b$

$T = F_b - W = 0.8\rho_{wat}\pi r^2 h g - \rho_{cyl}\pi r^2 h g =(0.8\rho_{wat} - \rho_{cyl})\pi r^2 h g$

and you can work that out with the given quantities.