A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
A uniform rigid beam AB has mass 20 kg and is 4m long. It rests on the fulcrum F and FB is 1 m. A 5 kg mass hangs from A and a vertical wire attached to the beam midway between F and B prevents the beam from rotating. Calculate the tension in the wire in Newtons.
anonymous
 5 years ago
A uniform rigid beam AB has mass 20 kg and is 4m long. It rests on the fulcrum F and FB is 1 m. A 5 kg mass hangs from A and a vertical wire attached to the beam midway between F and B prevents the beam from rotating. Calculate the tension in the wire in Newtons.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Take the balance of torque around F, letting clockwise be the positive direction and A be to the left of F. First, we should draw a free body diagram. dw:1327513578224:dw Let's note some lengths. \[\left(\begin{matrix}L_{AF} = 1 \\ L_{AC} = 0.5 \\ L_{FB} = 3 \\ L_{FD} = 1.5\end{matrix}\right)\]Second, we need to find the mass distribution of the beam on a per unit length basis. \[w = {m \over L} = {20 \over 4} = 5 ~\left[ \rm kg \over m \right]\]Now, we need to find the center of gravity of the portion of the beam to the left and right of the fulcrum. \[CG_{AF} = 0.5 [{\rm m}]\]\[CG_{FB} = 1.5 ~ [\rm m]\]Now, let's find the resultant force of the beam's mass distribution, which acts at the center of gravity. \[R_{AF} = L_{AF} \cdot w \cdot g \approx 50 ~ [\rm N]\]\[R_{FB} = L_{FB} \cdot w \cdot g \approx 150 ~[\rm N]\]Now, we can balance the torque. \[\sum \tau_F = 0 = (m_A \cdot g \cdot L_{AF})  (R_{AF} \cdot CG_{AF}) + (R_{FB} \cdot CG_{FB})  \left(T \cdot {L_{FB} \over 2} \right)\]This, of course, assumes the tension in the wire, \(T\) acts upwards. If we get a negative value for \(T\), we know it acts downwards.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.