The figure below (a) shows a sphere with a radius of r = 157 mm (density ñ = 1.24 g/cm³) suspended in water by a string. The ball is completely submerged in the water and the string is attached from the bottom of the water tank to the bottom of the sphere. What is the tension in the string?
i know that after doing the freebody diagram that it is F-W-T=0 since the sphere is not moving. So T=Fbuoyant-W
--> (density of fluid-density of sphere)gravity*volume of object?
Something doesn't make sense to me here. With a density of 1.24 g/cm^3, the weight of the sphere is greater than the buoyancy force. It should sink to the bottom of the tank. What good is a string at the bottom of the tank?
Your equations are correct.
To find the tension in the string, you are correct in using the equation F - W - T = 0, where F is the buoyant force, W is the weight, and T is the tension in the string. You can start by calculating the buoyant force.
The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
To calculate the buoyant force, you need to know the density of the fluid (water) and the volume of the object (sphere).
The density of water is approximately 1 g/cm³. Given that the sphere is completely submerged in water, the volume of the sphere is equal to its volume, which can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r³
where r is the radius of the sphere.
Given that r = 157 mm, which is equal to 15.7 cm, you can substitute this value into the formula to find the volume of the sphere.
Next, you need to calculate the weight of the sphere, which is given by W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).
The mass of the sphere can be calculated using the formula m = density * V, where the density of the sphere is given as 1.24 g/cm³.
Now that you have calculated the buoyant force (F) and the weight of the sphere (W), you can substitute these values into the equation F - W - T = 0 to find the tension in the string (T).
T = F - W
Therefore, the tension in the string can be calculated by subtracting the weight of the sphere from the buoyant force.
Keep in mind to convert the units to maintain consistency throughout the calculations.