# Statics question: calculate forces and reactions in tow-truck problem

• neeboy74
In summary: By setting the sum of forces and moments equal to zero, we were able to calculate the forces in each member and the reactions at points A and B.
neeboy74

## Homework Statement

"A lifting mechanism is mounted on the back of a truck as shown: Calculate the forces in each member and the reactions @ A & B for alpha=0

## Homework Equations

0=(5000N)(1m)+(-5000N)(-1.25m)+(By)(.5m)
By=2500N

## The Attempt at a Solution

I treated the entire assembly as a rigid body to get the force By above; that would make Ay=2500N, correct?

I have drawn the entire FDB in AutoCAD, and have found the following:

BD=6250N
CD=3750N
AB=2500N
AC=5590.167N
BC=5000N

I have attached a scan of the problem. Now, having said all of that, is my general thinking ok? We're supposed to be able to figure out the reactions @ A and B using the method of joints, but I'm having real trouble with that. I found the reactions by using moments around A and then summing my forces in the Y direction=0, and got my forces in the members by using trig, but I also need to figure out which members are in tension/compression, again, using method of joints. If someone could step me through finding the forces at any two joints, I think that in itself would be a very helpful start! Thanks in advance for any/all helpful replies

#### Attachments

• towtruckproblemscan.jpg
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!"

I would like to offer some suggestions and clarifications on the problem at hand. First, it is important to note that the given problem is a statics problem, meaning that the system is in equilibrium and all forces are balanced. This means that the sum of all the forces must equal zero, and the sum of all the moments (torques) must also equal zero.

To begin, I would recommend labeling all the forces and distances in the problem to avoid confusion. From the given information, we know that the system is at rest, and therefore the sum of all the forces must equal zero. This means that the forces in the x and y direction must be balanced. We also know that the sum of the moments about point A must equal zero, as stated in the problem.

To find the forces in each member, we can use the method of joints. This method involves isolating each joint and analyzing the forces acting on it. We can start by analyzing joint A. Since the system is in equilibrium, the forces acting on joint A must also be balanced. This means that the force in member AB must be equal and opposite to the force in member AC. We can use trigonometry to find the force in member AC, which is the hypotenuse of a right triangle with sides of 1.25m and 0.5m. The force in AC is then calculated to be approximately 5,590.2N.

Next, we can move on to joint B. Again, the forces acting on this joint must be balanced, so the force in member BC must be equal and opposite to the force in member BD. Using trigonometry, we can find the force in member BC to be approximately 5,000N.

Finally, we can use the sum of moments about point A to find the reaction forces at A and B. Since the system is in equilibrium, the sum of moments about any point must equal zero. This means that the moment caused by the force in member AB must be equal and opposite to the moment caused by the force in member AC. Similarly, the moment caused by the force in member BC must be equal and opposite to the moment caused by the force in member BD. We can use these relationships to find the reaction forces at points A and B.

In summary, to solve this problem we used the methods of equilibrium and joints to analyze the forces and reactions in the given system

."

I would start by saying that the problem description and equations provided seem to be correct and the method used to find the forces and reactions is also appropriate. However, there are a few things that could be clarified or added to the solution to make it more thorough and accurate.

Firstly, it would be helpful to mention that the forces in each member were found using the method of joints, as this is the main focus of the problem. Additionally, it would be helpful to provide a brief explanation of the method of joints and how it was used to find the forces in each member.

Regarding the reactions at A and B, it would be helpful to mention that these were found using the method of moments and the sum of forces in the y-direction, as this is not explicitly stated in the solution. Additionally, it would be beneficial to include a brief explanation of how these reactions were found and why they are important in the problem.

In terms of finding the forces at any two joints using the method of joints, it would be helpful to provide a step-by-step explanation of the process, including how to determine the forces in each member and whether they are in tension or compression. This could also be accompanied by a diagram or illustration to help visualize the process.

Overall, the solution provided is a good start, but could benefit from some additional clarification and explanation to make it more thorough and helpful for understanding the problem. It is important to clearly state the methods used and provide a step-by-step explanation of the process to ensure a complete and accurate solution.

## What is the purpose of calculating forces and reactions in a tow-truck problem?

The purpose of calculating forces and reactions in a tow-truck problem is to determine the magnitude and direction of the forces acting on the truck and the ground, as well as the reaction forces at the points of contact. This information is crucial in understanding the stability and safety of the truck and its ability to successfully tow another vehicle.

## What are the different types of forces involved in a tow-truck problem?

The different types of forces involved in a tow-truck problem are the weight of the truck and the towed vehicle, the tension in the tow cable, and the reaction forces at the points of contact between the truck and the ground.

## How do I calculate the forces and reactions in a tow-truck problem?

To calculate the forces and reactions in a tow-truck problem, you will need to draw a free body diagram of the truck and the towed vehicle. Then, you can use Newton's laws of motion and the equations of equilibrium to solve for the unknown forces and reactions.

## What assumptions are typically made when solving a tow-truck problem?

Some common assumptions made when solving a tow-truck problem are that the truck and towed vehicle are in a state of static equilibrium, the tow cable is ideal and has no mass, and the truck and ground are rigid bodies with no deformations.

## Are there any real-life applications of solving tow-truck problems?

Yes, there are many real-life applications of solving tow-truck problems. For example, engineers and mechanics use these principles to design and test the strength of tow trucks, and to ensure that they can safely tow heavy vehicles without toppling over. This type of analysis is also important in understanding the safety and stability of other heavy machinery and structures.

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