A ferry boat is 4.9 m wide and 6.9 m long.
When a truck pulls onto it, the boat sinks
3.34 cm in the water.
What is the weight of the truck? The
acceleration of gravity is 9.81 m/s2 .
To find the weight of the truck, we can use the concept of buoyancy and Archimedes' principle.
First, let's calculate the volume of water displaced by the submerged part of the boat. We can assume that the boat is shaped like a rectangular box with dimensions 4.9 m (width), 6.9 m (length), and 0.0334 m (depth of submersion).
The volume (V) of the submerged part of the boat can be calculated as:
V = width * length * depth
V = 4.9 m * 6.9 m * 0.0334 m
V ≈ 1.131 m³
According to Archimedes' principle, the buoyant force (Fb) acting on the submerged object is equal to the weight of the displaced water.
The weight of the displaced water can be calculated using the formula:
Weight = mass * gravity
Since we know the density of water is approximately 1000 kg/m³, we can calculate the mass of the water displaced:
Mass = density * volume
Mass = 1000 kg/m³ * 1.131 m³
Mass ≈ 1131 kg
Therefore, the weight of the displaced water is:
Weight = Mass * gravity
Weight = 1131 kg * 9.81 m/s²
Weight ≈ 11100.11 N
Since the buoyant force on the boat is equal to the weight of the displaced water, it must also be equal to the weight of the truck. Therefore, we can say that the weight of the truck is approximately 11100.11 N.