Don't get this dynamics problem

  • Thread starter elpermic
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    Dynamics
In summary, the conversation discusses finding the tension in two segments of a rope attached to a 100 N crate suspended from a ceiling. The solution involves drawing a diagram and using trigonometry to calculate the tension in each segment, resulting in estimated values of 82N and 58N. The use of the Sin Rule is also suggested as a method for confirming the results.
  • #1
elpermic
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Homework Statement



the ends of a rope are fastened to two hooks on a horizontal ceiling. A 100 N crate is attached to the rope so that the two segments of the rope make angles of 35 and 55 degrees with the horizontal. Determine the tension in each segment



Homework Equations



F=ma

The Attempt at a Solution



I don't get what to do.. I know a force on the crate is mg. I don't know where to put T1 and T2 for the segments of the rope. Do I also put mg on the segments of the rope?
 
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  • #2
Draw the diagram. Resolve T1 and T2 into vertical and horizontal components. In equilibrium condition, Horizontal components cancel each other and vertical components add up to mg. Solve these two equations to find T1 and T2.
 
  • #3
I get them as 82N and 58N? Anything close to what you get?

The crate is already given to you in Newtons, So no need to add gravity as it is already a force... If it was in kg, then you need to mulitply it by gravity.

My Solution:

Doesnt even need calculations ;) Although, it only gives a rough estimate...
Take the diagram and draw it out,

VectorDiagram1.jpg


You have one known vector there and 2 angles, 100N with 35' and 55'. So take the 100N as it is vertical and draw it vertically.

You also know that both the ties are holding it UP, so they will both be in an upwards direction in that picture. So take the 55' and draw it from the bottom of the 100N, and the 35' from the top of the 100N.

If you've drawn it accuratly and to scale, just measure off the rough figures. Like:

VectorDiagram2.jpg


I drew the one I have on a piece of paper at 1mm = 2N so I had a 5cm line as my 100N.

You can even confirm your results using the Sin Rule:

[tex]

\frac{A}{Sin a}

[/tex]= [tex]

\frac{B}{Sin b}

[/tex] = [tex]

\frac{C}{Sin c}

[/tex]

Therefore A = [tex]

\frac{100 X Sin55}{Sin90}

[/tex] = 81.92N

and B = [tex]

\frac{100 X Sin35}{Sin90}

[/tex] = 57.36N

X = Multiply...

Pretty close for a shoddy protracter and ruler!

(I apologise for my rubbish drawings as I do not have my tablet with me. And if my equations look weird, I am not sure how formatting fractions works on this forum!)

Hope it helps and you can understand my methods. Oh, And if anyone spots any mistakes or I am generally wrong feel free to bring me up on it :)
 
Last edited:

1. What is a dynamics problem?

A dynamics problem is a type of physics problem that involves the study of motion, forces, and energy in a system. It can range from simple problems such as calculating the acceleration of an object to more complex problems involving multiple objects and forces.

2. Why are dynamics problems difficult?

Dynamics problems can be difficult because they often require a solid understanding of fundamental concepts such as Newton's laws of motion and the principles of conservation of energy and momentum. They also often involve complex mathematical equations and require critical thinking skills to solve.

3. How can I improve my skills in solving dynamics problems?

One way to improve your skills in solving dynamics problems is to practice regularly and familiarize yourself with the fundamental concepts and equations. Seeking help from a tutor or participating in study groups can also be helpful in understanding and solving more challenging problems.

4. What are some common mistakes to avoid when solving dynamics problems?

One common mistake is not clearly defining the system and properly identifying and accounting for all the forces acting on the system. It is also important to pay attention to units and make sure they are consistent throughout the problem. Additionally, not double-checking calculations and assuming incorrect values can lead to errors in the final answer.

5. Are dynamics problems only applicable to physics?

No, dynamics problems can also be applied to other fields such as engineering, biomechanics, and even economics. The principles of dynamics can be used to analyze and understand the behavior of various systems and phenomena in these fields.

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