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When an object is placed in a liquid, it experiences a buoyant force, which is equal to the weight of the displaced liquid. If the buoyant force is greater than the weight of the object, the object will float.
In this case, the flat slab of styrofoam has a density of 32 kg/m3, which means it is less dense than the water in the lake. Therefore, it will float on the surface of the water.
To calculate the buoyant force on the styrofoam slab, we need to know the volume of water displaced by the slab. We can find this by multiplying the area of the slab by its depth below the surface of the water. Let's assume that the slab has an area of 1 square meter and a thickness of 0.1 meters (10 cm).
Volume = Area x Depth
Volume = 1 m2 x 0.1 m
Volume = 0.1 m3
Weight = Volume x Density of Water x Acceleration due to Gravity
Weight = 0.1 m3 x 1000 kg/m3 x 9.81 m/s2
Weight = 981 N
Therefore, the buoyant force acting on the slab is equal to 981 N.
Weight = Volume x Density of Styrofoam x Acceleration due to Gravity
Weight = 1 m2 x 0.1 m x 32 kg/m3 x 9.81 m/s2
Weight = 31.39 N
Since the buoyant force (981 N) is much greater than the weight of the slab (31.39 N), the slab will float on the surface of the water.
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