A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.50 cm into the river. What is the weight of the truck?
V = L*W*h = 6*4*0.045 = 1.08 m^3 = Vol.
of water displaced.
Mass=V * Dw=1.08m^3 * 1000kg/m^3=1080 kg
=Mass of water displaced=Mass of truck.
Wc = 1080kg * 9.8N/kg = 10,584 N. = Wt of the truck.
Fb - mg = 0
Fb = mg
PgV = mg
(1000)(9.8)(6)(4)(.04)
mg = 9408 N
Oh buoy, that's a sinking situation! Let's float some calculations and find the weight of the truck, shall we?
First, let's consider the volume of water displaced when the truck is on the boat. The boat sinks an additional 4.50 cm, which is equivalent to 0.045 m.
The volume of water displaced is the length multiplied by the width multiplied by the additional sinking depth. So, the volume is 6.00 m * 4.00 m * 0.045 m = 1.08 cubic meters.
Now, for the weight of water displaced, we need to consider the density of water, which is about 1000 kg/m^3. The weight of water displaced is the volume multiplied by the density, so it's 1.08 m^3 * 1000 kg/m^3 = 1080 kg.
Finally, the weight of the truck is equal to the weight of water displaced. Therefore, the weight of the truck is around 1080 kg.
Now that we've solved the weighty matter, I hope this answer floats your boat!
To find the weight of the truck, we need to calculate the buoyant force acting on the boat.
Step 1: Determine the volume of the boat that is submerged.
The volume of the boat that is submerged is given by the formula:
Volume = length * width * submerged depth
Substituting the given values, we get:
Volume = 6.00 m * 4.00 m * 0.045 m
Volume = 1.08 m³
Step 2: Determine the density of water.
The density of water is approximately 1000 kg/m³.
Step 3: Calculate the weight of the water displaced by the submerged part of the boat.
The weight of the water displaced is equal to the density of water multiplied by the volume submerged:
Weight of water displaced = volume * density of water
Weight of water displaced = 1.08 m³ * 1000 kg/m³
Weight of water displaced = 1080 kg
Step 4: Calculate the buoyant force.
The buoyant force is equal to the weight of the water displaced, which is given by:
Buoyant force = Weight of water displaced
Buoyant force = 1080 kg
Step 5: Calculate the weight of the truck.
Since the buoyant force is equal to the weight of the truck, we have:
Weight of truck = Buoyant force
Weight of truck = 1080 kg
Therefore, the weight of the truck is 1080 kg.
To determine the weight of the truck, we need to 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.
To calculate the weight of the truck, we can follow these steps:
Step 1: Calculate the volume of water displaced by the boat sinking:
The boat sinks an additional 4.50 cm into the river, so the volume of water displaced by the boat can be calculated as follows:
Volume of water displaced = width × length × depth
Width = 4.00 m
Length = 6.00 m
Depth = 4.50 cm = 0.045 m
Volume of water displaced = 4.00 m × 6.00 m × 0.045 m = 1.08 m³
Step 2: Calculate the weight of the water displaced:
To calculate the weight of the water displaced, we need to multiply the volume (1.08 m³) by the density of water (1000 kg/m³):
Weight of water displaced = Volume of water displaced × Density of water
Density of water = 1000 kg/m³
Weight of water displaced = 1.08 m³ × 1000 kg/m³ = 1080 kg
Step 3: Calculate the weight of the truck:
The weight of the truck is equal to the weight of the water displaced by the boat. Therefore, the weight of the truck is also 1080 kg.