A solid object has a weight of 13.62 N. When it is suspended from a scale and submerged in water, the scale reads 1.54 N. Find the density of the object (use pwater = 1000 kg/m3).
To find the density of the object, we need to use the concept of buoyancy.
When an object is submerged in a fluid, it experiences a buoyant force that counteracts the force of gravity. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.
In this case, the weight of the object in air is 13.62 N, and when submerged, the scale reads 1.54 N. The difference between these two values (13.62 N - 1.54 N = 12.08 N) represents the buoyant force acting on the object.
To calculate the density of the object, we can use the equation:
Buoyant force = Weight of the fluid displaced
Density of the fluid × Volume of the object × Acceleration due to gravity = Weight of the fluid displaced
We know the density of water (pwater = 1000 kg/m3) and the acceleration due to gravity (g = 9.8 m/s2).
Let's assume the volume of the object is V m3.
From the equation above, we can rewrite it as:
1000 kg/m3 × V m3 × 9.8 m/s2 = 12.08 N
Rearranging the equation to solve for V:
V = 12.08 N / (1000 kg/m3 × 9.8 m/s2)
V ≈ 0.001237 m3
Now that we know the volume of the object, we can find its density using the equation:
Density = Mass / Volume
To find the mass, we can use the equation:
Weight = Mass × Acceleration due to gravity
13.62 N = Mass × 9.8 m/s2
Solving for the mass:
Mass = 13.62 N / 9.8 m/s2 ≈ 1.39 kg
Now we can calculate the density:
Density = 1.39 kg / 0.001237 m3 ≈ 1122 kg/m3
Therefore, the density of the object is approximately 1122 kg/m3.