A 70-kg ancient statue lies at the bottom of the sea. Its volume is 3.0 x 104 cm3. How much force is needed to lift it?

To solve this problem, we need to consider two forces: the force of gravity acting on the statue and the buoyant force acting on the statue due to the water.

1. Calculate the force of gravity: The force of gravity (weight) can be calculated using the formula F = m*g, where m is the mass and g is the acceleration due to gravity. Here, m = 70 kg and g = 9.8 m/s² (approximate value on Earth's surface). So, F = 70 kg * 9.8 m/s² = 686 N. This is the force pulling the statue downwards.

2. Calculate the buoyant force: The buoyant force can be calculated using the formula F = ρVg, where ρ is the density of the fluid (in this case, sea water), V is the volume of the fluid displaced by the object, and g is the acceleration due to gravity. The density of sea water is approximately 1030 kg/m³. The volume of the statue is given in cm³, so we need to convert it to m³: 3.0 x 10^4 cm³ = 3.0 x 10^-2 m³. So, the buoyant force is F = 1030 kg/m³ * 3.0 x 10^-2 m³ * 9.8 m/s² = 302.82 N. This is the force pushing the statue upwards.

3. Calculate the net force: The net force needed to lift the statue is the difference between the force of gravity and the buoyant force: 686 N - 302.82 N = 383.18 N.

So, a force of approximately 383.18 N is needed to lift the statue.