A small cube is stacked on top of a big cube. The big cube is 0.5 m on a side. The small cube is 0.2 m on a side. The density of the material the cubes are made of is 1 kg/l . What is the pressure exerted on the ground by the cubes? The acceleration of gravity is 9.81 m/s2.
First, calculate the total volume of each cube. Since the big cube is 0.5 m on a side, that means it is 5 decimeters on a side. The volume is thus 125 dm3. 1 liter is 1 dm3, so the volume of the big cube is 125 liters. The volume of the small cube is likewise 8 liters. Since the density is 1 kg/l, the total weight of both cubes is (1 kg/l) x (133 l) = 133 kg. In order to determine the force this places on the earth, we must multiply the mass by the acceleration of gravity (force = mass x acceleration): F = 133 kg x 9.81 m/s2 = 1305 (kg m/s2) or 1305 Newtons. Pressure is the force per unit area. The area of the box that is on the earth (the big box in this case) is 0.5 x 0.5 m2 or 0.25 m2. (1305 N)/(0.25 m2) = 5219 N/m2 or 5219 Pa.