Calculate Tension in Rope: Principle of Moments Homework

[Marcus27]

Homework Statement

Calculate the tension in the rope, T, in the diagram below: http://imageshack.com/a/img905/2848/yMC01l.png

Homework Equations

The Attempt at a Solution

The 'beam' is a stable structure, thus the resultant forces be equal that are acting upon the beam. So,
I calculated the the Torque from the mass as being 150N * 0.6m + 100N * 0.3m = 110 Nm, setting this equal to the Torque generated by the 'force line' from the rope, T*1.2m = 110Nm, thus T rounded to the nearest Newton is = 92N. I Felt fairly confident with this until my textbook said the tension in the rope is = to 100N. Can anybody clear this up for me and explain where I went wrong, Thanks!.

 

[Bystander]

150N * 0.6m + 100N * 0.3m = 110 Nm

Check your arithmetic, that's "the usual suspect."

 

[Marcus27]

Ah, thank you. I did not spot that mistake, sorry for wasting your time. Not a great first post on my part

 

[Bystander]

Do not let it ruin your day --- we've all been there.

 

[HalfLostAndSearching]

Dear student,

Your approach to calculating the tension in the rope is correct. The principle of moments states that the sum of clockwise moments must be equal to the sum of counterclockwise moments in a stable structure. In this case, the clockwise moment is generated by the weight of the mass (150N * 0.6m + 100N * 0.3m) and the counterclockwise moment is generated by the tension in the rope (T * 1.2m). Setting these two moments equal to each other, we can solve for T and get a value of 92N, as you did.

It is possible that your textbook has a different value for the weight of the mass (e.g. 120N instead of 150N), which would result in a different value for the tension in the rope. It is also possible that there is a rounding error in the textbook's answer.

In any case, your approach is correct and you should feel confident in your solution. Keep up the good work in your studies of physics!

Best regards,