# Calculate Truck Weight on Ferry Sinkage: Solved

• 7starmantis
In summary, when a truck drives onto a river ferry, the ferry sinks. The weight of the truck is equal to the displaced water volume.
7starmantis
[SOLVED] Floating Weight

When a truck drives onto a river ferry the ferry sinks 0.0367M. The length and width of the ferry are 15.24M and 6.10M respectively. Determine the weight of the truck.
Just not quite sure I'm setting it up correctly, or getting the right answer.
I originally thought of using the pressure equation (p=pgh) to find the pressure at the new "depth" and using that in the force equation (F=P/A) to find the Force. That doesn't really make sense though, right?

Just plain old Archimedes' Principle will do in this case. Extra buoyant force to take the weight of the lorry = extra water displaced.

So we are looking at something like:

Buoyant Force only changes once the truck drives onto the ferry. So the displaced water equals the weight of the truck? That would mean...

Buoyant force (wt of truck) = P2A - P1A
P1 - ATM pressure
P2 = $$\rho$$gh
A = length X width

so...

= ($$\rho$$gh)A - (ATM Pressure)A
= (1000)(9.8)(.0367m)(93m^2) - (1.013 X10^5 Pa)(93m^2)
= 33448.37 - 9420900
But that gives a negative number?

"pressure" has nothing to do with this. If the ferry is 125.4 m by 6.10 m and sinks 0.0367 m, what volume of water was displaced? How much did that water weigh?

(If you are using air pressure to calculate the force of the air on the ferry, remember that was their before the truck moved onto the ferry and is already accounted for.)

This is making me feel really stupid.
I understand the concept that the water displaced will equal the weight of the truck, but I can't seem to find an equation to find that mass of the water.
I can't determine the volume or weight of the ferry.

Could I not find the pressure at that depth by $$\rho$$gh
(1000)(9.8)(.0367) = 359.7pa
F = PA
= (359.7)(15.24m X 6.10m)
= 33439.2 / 9.8
= 3412.16 kg ?

7starmantis said:
I understand the concept that the water displaced will equal the weight of the truck, but I can't seem to find an equation to find that mass of the water.
I can't determine the volume or weight of the ferry.

The cross-sectional area of the ferry is given. It is sinking by a certain height. So, vol of water displaced = area*height. Vol*density gives you mass, and mass*g gives you weight.

Now you can apply Archimedes' Principle.

Ok, so Vol of water displaced is:

vol = a*h
= (15.24X6.10)*(.0367)
= 3.41m^3

Then:
m = v*$$\rho$$
= (3.41)*(1000)
= 3410kg

Wt = 3410kg * 9.8 = 33418N

So that is the weight of the water displaced which is also the weight of the truck.
That makes sense to me. Why couldn't I figure that out before I have no idea.
Does that seem right?

Last edited:
Very much so (but I haven't checked your arithmetic).

Thats ok, I just wanted to understand the concept and make sure I was setting it up right.(although it does sound like a big weight)

Thank you very much for your help, you explained it in a way I could understand. I really appreciate it! a lot!

## 1. How do you calculate the weight of a truck on a ferry?

To calculate the weight of a truck on a ferry, you will need to know the weight of the truck and the weight of the ferry. You will also need to know the distance between the axles of the truck and the distance between the axles of the ferry. Then, you can use the formula Wt = (Wf x Lt) / Lf, where Wt is the weight of the truck on the ferry, Wf is the weight of the truck, Lt is the distance between the axles of the truck, and Lf is the distance between the axles of the ferry.

## 2. What is the purpose of calculating truck weight on ferry sinkage?

The purpose of calculating truck weight on ferry sinkage is to ensure that the ferry is not overloaded and will not sink under the weight of the truck. It is important to accurately calculate the weight of the truck on the ferry to ensure the safety of all passengers and cargo on board.

## 3. What factors can affect the accuracy of the truck weight on ferry sinkage calculation?

There are several factors that can affect the accuracy of the truck weight on ferry sinkage calculation. These include changes in the weight of the truck, changes in the weight distribution within the truck, changes in the weight of the ferry, changes in the weight distribution within the ferry, and changes in the distance between the axles of the truck and the ferry.

## 4. How can you ensure the accuracy of the truck weight on ferry sinkage calculation?

To ensure the accuracy of the truck weight on ferry sinkage calculation, it is important to use precise measurements of the weight and distance of both the truck and the ferry. It is also important to regularly check and update these measurements as they may change over time. Additionally, using a reliable and accurate formula or calculator can help ensure the accuracy of the calculation.

## 5. Are there any safety precautions that should be taken when calculating truck weight on ferry sinkage?

Yes, there are several safety precautions that should be taken when calculating truck weight on ferry sinkage. These include making sure that the truck is parked securely on the ferry, that all passengers and cargo are properly distributed on the ferry, and that the weight of the truck does not exceed the weight capacity of the ferry. It is also important to regularly monitor the weight and distribution of the truck and ferry throughout the journey to ensure the safety of everyone on board.

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