A hollow steel buoy in thee form of a sphere of radius 0.5m is fixed by a wire to the base of a river. If the mass of the buoy is 20kg, calculate the tension in the cable. (Take density of water=1000 kilograms per cubic meter).
5036N
physics
5036
𝚂𝚘𝚛𝚛𝚢 𝚠𝚑𝚊𝚝 𝚏𝚘𝚛𝚖𝚞𝚕𝚊 𝚍𝚒𝚍 𝚢𝚘𝚞 𝚞𝚜𝚎𝚍 𝚝𝚘 𝚌𝚊𝚕𝚌𝚞𝚕𝚊𝚝𝚎 𝚠𝚒𝚝𝚑?
To calculate the tension in the cable, we need to consider the buoyancy force acting on the hollow steel buoy. The buoyant force is equal to the weight of the water displaced by the buoy.
1. First, let's find the volume of the steel buoy. The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere.
Plugging in the given radius of 0.5m, we have V = (4/3)π(0.5^3) = 0.5236 cubic meters.
2. Since the buoyancy force is equal to the weight of the water displaced, we need to find the weight of the water displaced by the buoy. The weight can be calculated using the formula weight = mass * gravity, where the mass is the volume of water displaced multiplied by its density, and gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
The mass of water displaced can be found using the formula mass = density * volume, where the density of water, as given, is 1000 kg/m^3.
Plugging in the values, we have mass = 1000 kg/m^3 * 0.5236 m^3 = 523.6 kg.
Therefore, the weight of the water displaced is weight = mass * gravity = 523.6 kg * 9.8 m/s^2 = 5131.28 N.
3. Now, let's consider the tension in the cable. The tension in the cable is equal to the sum of the buoyant force acting upward and the weight of the buoy acting downward.
Since the weight of the buoy is given as 20 kg, the weight of the buoy is weight = mass * gravity = 20 kg * 9.8 m/s^2 = 196 N.
4. Finally, we can find the tension in the cable by adding the weight of the water displaced to the weight of the buoy.
Tension = weight of the water displaced + weight of the buoy = 5131.28 N + 196 N = 5327.28 N.
Therefore, the tension in the cable is approximately 5327.28 N.