A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat sinks 4.00 cm in the water. What is the combined weight of the truck and the ferry?
9.4*10^3N
To find the combined weight of the truck and the ferry, we can use the concept of buoyancy. When an object is placed in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.
In this case, the boat sinks by 4.00 cm when the truck pulls onto it. This sinking can be seen as the boat displacing water equal to its own weight plus the weight of the truck. Therefore, we can calculate the weight of the boat and the truck by finding the weight of the water displaced by the boat sinking.
First, let's calculate the volume of water displaced. The volume of a rectangular prism (in this case, the boat) is given by the formula V = length x width x height. Since the boat sinks by 4.00 cm in the water, the height of the displaced water is 4.00 cm.
V = 6.0 m x 4.0 m x 0.04 m (converting cm to m)
= 0.96 m³
Now, we need to find the weight of the water displaced. The weight of an object can be calculated using the formula W = m x g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).
The mass of the water can be found using the density formula, which is ρ = m/V, where ρ is the density of water (approximately 1000 kg/m³).
ρ = 1000 kg/m³
V = 0.96 m³
m = ρ x V
= 1000 kg/m³ x 0.96 m³
= 960 kg
Now, we know that the weight of the displaced water is 960 kg. This buoyant force is equal to the combined weight of the boat and the truck.
Therefore, the combined weight of the truck and the ferry is 960 kg.