FBD of a loaded Dumptruck platform that is Tilting

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In summary, a conversation is had about drawing a free body diagram of a loaded truck platform and determining the meaning of forces. A moment equation is used, but there is a mistake in the calculation and the angle is corrected. The mistake in the moment equation is also found and corrected.
  • #1
Mech_LS24
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Homework Statement
Draw a FBD from the loaded platform of the truck. D has a mass of 25 kN and it's center is at point G. D rest on a pin in A and is connected with a hydraulic cylinder pinned in point B. Give the meaning of the forces.
Relevant Equations
Momentsum= 0;
Hi,

From the picture the following statement is asked:
"Draw a FBD from the loaded platform of the truck. D has a mass of 25 kN and it's center is at point G. D rest on a pin in A and is connected with a hydraulic cylinder pinned in point B. Give the meaning of the forces."

I made a FBD and I am curious doing it correctly, due to the missing answer at the book...
As well I added a momentsum about point A to find force Fbc, did I have done it both correct?

Thanks in advance!

1624101148898.png


1624101951352.png
 
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  • #2
The FBD is OK, but you will have to separate forces G and FBC into two components to be useful.

The moment equation is all wrong. Only the perpendicular component of a force with respect to the lever arm is relevant to the moment applied.
 
  • #3
Thanks,

Is this what you mean?:
1624182808485.jpeg
 
  • #4
I think you have a slight mistake in your moment equation, that sin60 should be sin50. That angle you mark as 60 degrees (with vertex B) is in fact equal to the sum of the opposite interior angles of that triangle. That is equal to 20+30=50.
And be careful at the algebra, the solution of that equation is NOT 2.97KN (even if we take the equation to be correct).
I solved the corrected moment equation and find ##F_{BC}\approx 18.81kN##
 
  • #5
Thanks for pointing me on that angle. A good lesson for me, I re-draw a sketch on scale and see the difference now (see below).

And I found my mistake in my moment equation. My calculator was in radians 😂.
1624205181711.jpeg
 
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1. What is the FBD of a loaded dumptruck platform that is tilting?

The FBD (free body diagram) of a loaded dumptruck platform that is tilting is a visual representation of all the forces acting on the platform. This includes the weight of the platform, the weight of the load, and any other external forces such as wind or friction.

2. Why is it important to understand the FBD of a loaded dumptruck platform that is tilting?

Understanding the FBD of a loaded dumptruck platform that is tilting is important because it allows us to analyze the forces acting on the platform and determine if it is stable or if there is a risk of tipping. This information is crucial for ensuring the safety of the dumptruck operator and nearby workers.

3. How do you create an FBD of a loaded dumptruck platform that is tilting?

To create an FBD of a loaded dumptruck platform that is tilting, you will need to identify all the forces acting on the platform and draw them as arrows on a diagram. Make sure to label each force with its magnitude and direction. You may also need to consider the dimensions and weight distribution of the platform to accurately represent the forces.

4. What factors can affect the FBD of a loaded dumptruck platform that is tilting?

There are several factors that can affect the FBD of a loaded dumptruck platform that is tilting. These include the weight and distribution of the load, the angle of the platform, the terrain and surface conditions, and any external forces such as wind or uneven ground.

5. How can the FBD of a loaded dumptruck platform that is tilting be used to improve safety?

By understanding the FBD of a loaded dumptruck platform that is tilting, safety measures can be implemented to prevent accidents. For example, if the FBD shows that the platform is at risk of tipping due to an uneven load distribution, steps can be taken to redistribute the load or adjust the angle of the platform to prevent tipping. Additionally, regular inspection and maintenance of the dumptruck and its components can also help ensure the safety of the operator and surrounding workers.

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