A ferry-boat is 4 m long and 6 m wide, and floats in fresh water. A 400kg horse is loaded onto the ferry. How much deeper will the ferry float when it is loaded with the horse? Show ALL of your work. Include units in your solution.
what volume of water has a mass of 400kg?
Divide that by 24m^2 to get the depth of the displaced water.
a cubic meter of water is a metric ton
... 1000 kg
.4 m^3 / 24 m^2
To find out how much deeper the ferry will float when loaded with the horse, we need to determine the change in buoyant force on the ferry.
1. First, let's calculate the initial volume of the ferry boat:
The volume of a rectangular object like the ferry can be determined by multiplying its length by its width and its height. However, since the height is not given, we can assume it to be negligible in this case.
Given:
Length of ferry = 4 m
Width of ferry = 6 m
Therefore, the initial volume of the ferry boat is:
Volume = Length * Width * Height
= 4 m * 6 m * 0 m (negligible height)
= 0 m³
2. Next, let's calculate the final volume when the horse is loaded onto the ferry:
Adding the horse to the ferry will displace water, increasing the overall volume. The additional volume is equal to the volume of the horse.
Given:
Mass of the horse = 400 kg
To find the volume of the horse, we can divide its mass by the density of water. The density of fresh water is approximately 1000 kg/m³.
Therefore, the volume of the horse is:
Volume = Mass / Density
= 400 kg / 1000 kg/m³
= 0.4 m³ (cubic meters)
The final volume of the ferry boat is the sum of its initial volume and the volume of the horse:
Final Volume = Initial Volume + Volume of Horse
= 0 m³ + 0.4 m³
= 0.4 m³
3. Now, let's calculate the change in buoyant force on the ferry:
The buoyant force acting on the ferry is equal to the weight of the water displaced by the ferry. According to Archimedes' principle, the buoyant force is directly proportional to the volume of water displaced.
Given:
Density of fresh water = 1000 kg/m³
The buoyant force can be calculated as:
Buoyant Force = Density of Fluid * Volume of Fluid Displaced * g (acceleration due to gravity)
= Density of Fresh Water * Change in Volume * g
= 1000 kg/m³ * 0.4 m³ * 9.8 m/s²
= 3920 N (Newtons)
4. Finally, let's calculate the change in depth or how much deeper the ferry will float:
The additional buoyant force on the ferry boat will cause it to float higher in the water, leading to a decrease in depth.
The change in depth can be calculated using Archimedes' principle:
Change in Depth = Change in Buoyant Force / (Area of the Water's Surface * Density of Fluid * g)
= Change in Buoyant Force / (Width of Ferry * Length of Ferry * Density of Fresh Water * g)
= 3920 N / (6 m * 4 m * 1000 kg/m³ * 9.8 m/s²)
= 0.106 m (meters) or 10.6 cm (centimeters)
So, the ferry will float approximately 10.6 centimeters (or 0.106 meters) deeper when loaded with the 400 kg horse.