A spherical buoy of radius 25 cm and mass 8 kg sits in sea water of density 1025 kg/m3

. At low
tide its anchoring chains have got tangled. What is the maximum tension force this chain may
have to withstand at high tide? Assume calm conditions.

To find the maximum tension force the anchoring chains may have to withstand at high tide, we need to consider the buoy's weight and the buoy's buoyant force.

1. Start by calculating the volume of the buoy using its radius:
Volume = (4/3) * π * r^3
Volume = (4/3) * 3.14 * (0.25)^3 m^3
Volume = 0.065449 m^3

2. The buoy's weight can be calculated using its mass and gravitational acceleration:
Weight = mass * gravitational acceleration
Weight = 8 kg * 9.8 m/s^2
Weight = 78.4 N

3. Next, calculate the buoyant force using the buoy's volume and the density of the sea water:
Buoyant force = volume * density * gravitational acceleration
Buoyant force = 0.065449 m^3 * 1025 kg/m^3 * 9.8 m/s^2
Buoyant force = 637.90 N

4. Finally, to find the maximum tension force the anchoring chains need to withstand, subtract the buoyant force from the buoy's weight:
Maximum tension force = Weight - Buoyant force
Maximum tension force = 78.4 N - 637.90 N
Maximum tension force = -559.50 N (Note: The negative sign indicates that the buoy is being pushed downwards.)

So, the maximum tension force the anchoring chains may have to withstand at high tide is approximately 559.50 N.