Drive the apparent weight of an object when a body of mass float's on a liquid density
Assuming the object is fully submerged and in equilibrium:
The apparent weight of an object floating on a liquid is equal to the weight of the displaced liquid. This is known as Archimedes' principle.
The buoyant force (FB) acting on the object is equal to the weight of the displaced liquid. This can be expressed as:
FB = ρ l Vg
where ρ l is the density of the liquid, V is the volume of the displaced liquid (equal to the volume of the object), and g is the gravitational acceleration.
The weight of the object (W) acting downwards is given by:
W = mg
where m is the mass of the object.
Thus, the apparent weight (Wa) of the object is:
Wa = W - FB
= mg - ρ l Vg
Simplifying this equation we get:
Wa = g(m - ρ l V)
Therefore, if the mass of the object is equal to the mass of the displaced liquid (m = ρ l V), then the apparent weight of the object will be zero. This is the condition for an object to float in equilibrium.
If the density of the object is greater than the density of the liquid (ρ o > ρ l), then the object will sink. In this case, the apparent weight of the object will be equal to the weight of the object itself (Wa = W = mg).
If the density of the object is less than the density of the liquid (ρ o < ρ l), then the object will float. In this case, the apparent weight of the object will be less than its actual weight (Wa < W).
To calculate the apparent weight of an object when it floats on a liquid, we need to consider the buoyant force acting on the object. Here are the step-by-step instructions:
Step 1: Determine the density of the liquid (ρL). This information can usually be found in the problem statement or given data.
Step 2: Find the mass of the object (m) using the given information.
Step 3: Calculate the volume of the submerged part of the object (Vsub) using the formula Vsub = m / ρL, where m is the mass of the object and ρL is the density of the liquid.
Step 4: Calculate the buoyant force (Fb) using the formula Fb = ρL * g * Vsub, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 5: Finally, calculate the apparent weight (W_apparent) of the object using the equation W_apparent = W - Fb, where W is the weight of the object (W = m * g).
By following these steps, you can determine the apparent weight of an object when it floats on a liquid.