# Solving Rod Slipping: Find x min with Tension & Friction

• eliassiguenza
In summary, a problem involving a uniform rod of length 4.0m and mass M supported by a cable under tension T and resting against a wall with a coefficient of static friction of 0.5. An additional mass M is hung from the rod at a distance x from the wall. The equations used to solve the problem are Mgx + 2Mg = 4TsinӨ, 2Mg = (R/2) + TsinӨ, and R = TcosӨ. The minimum value of x where the additional mass can be hung without causing the rod to slip is x = 2
eliassiguenza

## Homework Statement

a uniform rod of length 4.0m of mass M is supported by a cable which is under tension T. The other end rests against as wall, where it is held by friction. The coefficient of static friction is 0.5. An additional mass M is hung from the rod at a distance x from the wall

## Homework Equations

Mgx + 2 Mg = 4T sinӨ
2Mg = (R/2) + T sin Ө
R = T cos Ө

## The Attempt at a Solution

Solve the above three equations simultaneously for Ө = 37 to obtain the minimum value of x in metres where the additional mass M may be hung without causing the rod to slip.

Answer is : x min = 2.8 m

how do you solve this ? I am totally lost :'( please help I have an exam on monday next week :'(

Mgx + 2 Mg = 4T sinӨ
2Mg = (R/2) + T sin Ө
R = T cos Ө

The first equation looks good. How did you get the other two? The second looks like the equilibrium equation for the forces in the vertical direction, but it has mistakes in it.

The cable is horizontal ? Or is the rod horizontal ?
The additional mass "M" is equal to the rod mass "M" ?

The problem would be greatly clarified if a diagram could be provided. The orientation and location of attachment of the cable are unspecified, so the problem is not solvable.

To the OP: Do any of the cable positions, 1, 2, or 3 in the attached figure, correspond to the current problem?

#### Attachments

• Fig1.gif
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yes that's the diagram how silly of me! oh god i forgot... yeah that's the one! cable one is just like the red one

## 1. How does tension affect rod slipping?

Tension is a force that acts on an object in a direction that is opposite to the direction of motion. In the case of a slipping rod, tension can help to prevent the rod from slipping by creating a counteracting force that holds the rod in place. If the tension is too low, the rod may slip; if the tension is too high, the rod may break.

## 2. What role does friction play in solving for x min?

Friction is a force that opposes motion between two surfaces in contact. In the case of a slipping rod, friction can act in two ways: it can either increase or decrease the tension required to prevent slipping. To solve for x min, it is important to consider the amount of friction between the rod and the surface it is resting on.

## 3. How can I determine the minimum value of x to prevent rod slipping?

To determine the minimum value of x, you will need to use the equations of motion and Newton's laws of motion. By setting up an equation that takes into account the forces acting on the rod (including tension and friction), you can solve for x min. It is also important to consider any other factors that may affect the motion of the rod, such as the angle of the surface or the weight of the rod.

## 4. What assumptions are made when solving for x min with tension and friction?

When solving for x min, it is important to make certain assumptions about the system. For example, we may assume that the rod is a rigid body and that the surface it is resting on is flat and smooth. Additionally, we may assume that there are no other external forces acting on the rod besides tension and friction.

## 5. Are there any real-world applications for solving rod slipping with tension and friction?

Yes, there are many real-world applications for solving rod slipping with tension and friction. For example, engineers may use these principles when designing structures such as bridges or buildings, to ensure that they can withstand the forces acting on them. This type of problem-solving is also important in fields such as mechanics, physics, and materials science.

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