A box with a volume V = 0.03 m^3 lies at the bottom of a lake whose water has a density of 103 kg/m^3.

(a) How much force is required to lift the box, if the mass of the box is 100 kg?

(b) How much force is required to lift the box, if the mass of the box is 70 kg?

Check your density of water again.

103 kg/m^3 is much too low.

ah thanks, it's 10^3 kg/m^3

(a) The buoyancy force on the box is

V*(water density)*g = 294 Newtons

The box's mass is M g = 980 N

Force required to lift = 686 N

(b) same approach, but the box weighs 686 N
Force required to lift = 686 - 294

thank you very much!

300

N

To determine the force required to lift the box, we need to consider the weight of the box and the buoyant force acting on it. The weight of an object can be calculated using the formula:

Weight = mass * acceleration due to gravity

where the acceleration due to gravity is approximately 9.8 m/s^2.

To calculate the buoyant force, we need to consider the volume of the box submerged in water and the density of the water. The buoyant force can be calculated using the formula:

Buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity

where the volume of fluid displaced is equal to the volume of the box submerged in water.

(a) For a mass of 100 kg:
The weight of the box is given by:
Weight = 100 kg * 9.8 m/s^2 = 980 N

Given that the volume of the box is 0.03 m^3, and it is fully submerged in water, the volume of fluid displaced is also 0.03 m^3. The buoyant force can be calculated as follows:
Buoyant force = 103 kg/m^3 * 0.03 m^3 * 9.8 m/s^2 = 30.414 N

To lift the box, the net force applied must be equal to the sum of the weight and the buoyant force:
Force required = Weight + Buoyant force = 980 N + 30.414 N = 1010.414 N

Therefore, the force required to lift the box with a mass of 100 kg is approximately 1010.414 N.

(b) For a mass of 70 kg:
Following the same procedure, the weight of the box is given by:
Weight = 70 kg * 9.8 m/s^2 = 686 N

The volume of fluid displaced is still 0.03 m^3, and the buoyant force can be calculated as follows:
Buoyant force = 103 kg/m^3 * 0.03 m^3 * 9.8 m/s^2 = 30.414 N

To lift the box, the net force applied must be equal to the sum of the weight and the buoyant force:
Force required = Weight + Buoyant force = 686 N + 30.414 N = 716.414 N

Therefore, the force required to lift the box with a mass of 70 kg is approximately 716.414 N.