A 2.80kg block of copper with a height of 0.250m and an area of 1.26 X 10^2 is floating in a tub of liquid mercury. How far from the surface of the mercury is the bottom of the block? Hint: you need to start with Newton's second law
To find the distance from the surface of the mercury to the bottom of the block, we can use Newton's second law, which states that the sum of forces acting on an object is equal to its mass multiplied by its acceleration.
In this case, the block is floating, which means that it is in equilibrium, and the forces acting on it must balance out. There are two forces to consider: the weight of the block and the buoyant force exerted by the liquid mercury.
The weight of the block can be calculated using the equation:
Weight = mass * acceleration due to gravity
where mass is given as 2.80 kg and the acceleration due to gravity is approximately 9.8 m/s².
Weight = (2.80 kg) * (9.8 m/s²) = 27.44 N
The buoyant force can be calculated using the equation:
Buoyant force = density of liquid * volume of displaced liquid * acceleration due to gravity
The density of liquid mercury is given as 13,600 kg/m³, and the volume of displaced liquid can be calculated using the equation:
Volume = area * height
where the area is given as 1.26 × 10² m² and the height is given as 0.250 m.
Volume = (1.26 × 10² m²) * (0.250 m) = 31.5 m³
Now, we can calculate the buoyant force:
Buoyant force = (13,600 kg/m³) * (31.5 m³) * (9.8 m/s²) = 4,018,920 N
Since the block is in equilibrium, the weight of the block must be equal to the buoyant force. Therefore, the distance from the surface of the mercury to the bottom of the block can be found by dividing the weight by the buoyant force and multiplying it by the height of the block.
Distance = (Weight / Buoyant force) * Height
Distance = (27.44 N / 4,018,920 N) * (0.250 m) = 0.00171 m
Therefore, the bottom of the block is approximately 0.00171 meters or 1.71 millimeters from the surface of the mercury.