Equilibrium practice final exam problem

[Californiarol]

Homework Statement

A 17.674 kg 2.0m long horizontal uniform beam is hinged at one end and it is supported at the other end by a cable that makes an angle of 60 degrees to the horizontal.

Calculate the tension in the cable when it has been shortened so that the beam makes an angle of 60 degrees to the horizontal.

Homework Equations

$$\sum F_{x}=0$$

$$\sum F_{y}=0$$

$$\sum \tau=0$$

The Attempt at a Solution

After finding the equations using $$\sum F_{x}=0$$ and

$$\sum F_{y}=0$$, I realized that we only need that $$\sum \tau=0$$.

So working with that, I got

$$\sum \tau=0 \Rightarrow \1cos60*17.674*9.81-Tsin120*2=0$$

Solving for T would give T = 50.05 but the answer booklet says its 5.10. Any help would be appreciated. Thanks!

 

[anathema]

Thank you for your post. I believe the discrepancy in your calculation may be due to a few errors in your equations. Firstly, when using \sum \tau=0, the equation should be set equal to zero, so it should be written as:

\sum \tau = 0 \Rightarrow 1\cos60*17.674*9.81 - T\sin120*2 = 0

Additionally, when solving for T, the value for the cosine term should be 0.5, not 1. So the correct equation should be:

\sum \tau = 0 \Rightarrow 0.5*17.674*9.81 - T\sin120*2 = 0

Solving for T using this equation will give the correct answer of 5.10 N. I hope this helps. Remember to always double check your equations and units when solving physics problems. Good luck with your studies!

 

[kerimek]

I would first check to make sure that all units are consistent in the equation. It appears that you may have used the wrong unit for the length of the beam. Instead of using 2.0m, you may have used 2.0cm. This would result in a significantly smaller value for T.

I would also recommend double-checking your calculations to ensure that there are no errors. This could include rounding errors or mistakes in the trigonometric functions.

If the units and calculations are correct, then I would suggest considering any external forces that may be acting on the beam, such as the weight of the beam itself. This could affect the tension in the cable and result in a different value for T.

Overall, it is important to carefully check all aspects of the problem and calculations to ensure an accurate solution.