A duck is floating on water with 26% of its total volume submerged below the surface. If the duck has a mass of 2.6kg, what is the duck’s total volume? You must show all necessary work, the density of water is 1000kg/m3.
Let V be the volume of the duck.
Weight of displaced water = weight of the duck
0.26•V•ρ•g= mg
0.26•V•1000•g =mg
260 V = m
The density of the duck is
ρ= m/V= 260 V/V= 260 kg/m³
V= m/V=2.6/260=0.01 m³
To find the duck's total volume, we can use the concept of buoyancy.
First, let's begin by calculating the volume of water displaced by the duck.
We know that the density of water is 1000 kg/m^3, and 26% of the duck's total volume is submerged. This means that the water displaced has the same volume as the submerged portion of the duck.
Let's assume the total volume of the duck is V (in cubic meters). Then, the volume of water displaced is 0.26V (since 26% is submerged).
The weight of the water displaced is equal to the buoyant force acting on the duck, which is given by the formula:
Buoyant force = weight of the water displaced = density of water * volume of water displaced
Buoyant force = 1000 kg/m^3 * 0.26V m^3 = 260V kg
Since the buoyant force is equal to the weight of the duck, we have:
260V kg = 2.6 kg
Now, let's solve this equation to find the value of V, which represents the total volume of the duck:
V = 2.6 kg / 260 kg = 0.01 m^3
Therefore, the duck's total volume is 0.01 cubic meters.