A small rectangular ferry boat is 3.33 m wide
and 5.64 m long. When a loaded truck pulls
onto it, the boat sinks an additional 3.25 cm
into the river.
What is the weight of the truck? The acceleration of gravity is 9.8 m/s2 .
Answer in units of kN.
density of water = 1000 kg/m^3
if .0325 m = additional depth immersed
buoyancy volume added = 3.33*5.64*.0325
mass of water displaced = 3.33*5.64*32.5 kg
weigh of water displaced = m g
= 3.33*5.64*32.5*9.8 Newtons
= 5981 N
=5.981 kN
To find the weight of the truck, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The buoyant force can be calculated using the formula:
Buoyant force = density of the fluid x volume of the fluid displaced x acceleration due to gravity
First, we need to calculate the volume of the water displaced by the boat sinking. The volume of the water displaced is equal to the volume of the submerged part of the boat.
The submerged depth of the boat can be found by subtracting the additional sinkage from the depth of the boat:
Submerged depth = initial depth of the boat - additional sinkage
Submerged depth = 0.0325 m
The volume of the water displaced can be calculated using the formula:
Volume of water displaced = submerged depth x width x length
Volume of water displaced = 0.0325 m x 3.33 m x 5.64 m
Next, we need to calculate the weight of the truck using the formula:
Weight of the truck = buoyant force
To convert the weight from Newtons (N) to kilonewtons (kN), we need to divide the weight by 1000.
So, the weight of the truck in kN can be calculated as:
Weight of the truck = (density of water x volume of water displaced x acceleration due to gravity) / 1000
First, we need to find the density of water, which is approximately 1000 kg/m^3.
Weight of the truck = (1000 kg/m^3 x 0.0325 m x 3.33 m x 5.64 m x 9.8 m/s^2) / 1000
Now, we can calculate the weight of the truck by plugging in the values into the equation.
Weight of the truck = 567.432 kN
Therefore, the weight of the truck is approximately 567.432 kN.