A bag of cement of weight Fg hangs from three wires as .....??
A bag of cement of weight Fg hangs from three wires as shown in the
attached diagram (link). Two of the wires make angles theta1 and theta2
with the horizontal. If the system were in equilibrium, show that the
tension in the left hand wire is: T1 = (Fg.costheta2) /
sin(theta 1 + theta2)
Thanks !!
/>http://picasaweb..com/dasaman2007/UntitledAlbum#5385936682639506130
Because the system is in equilibrium & there is no
acceleration, we can deduce the following:
T3 is balancing the weight. Therefore, T3 = Fg ----> (1)
Horizontal components of T1 & T2 are balancing each other. Therefore,
T1costheta1 = T2costheta2 ----> (2) And, finally vertical components of T1 & T2 are balancing T3. Therefore, T1sintheta1 + T2sintheta2 = T3 ----> (3) Now we have three equations, to get what is required, we just have to manipulate those equations & eliminate T2 & T3, because these terms don't appear in the required equation. T1costheta1 = T2costheta2 => T2 = T1costheta1 / costheta2 Putting this value in eq (3), T1sintheta1 + (T1costheta1 / costheta2)sintheta2 = Fg => T1 [ sintheta1costheta2 + costheta1sintheta2 ] = Fgcostheta2 => T1[sin(theta1 + theta2)] = Fgcostheta2 (Because, sin(a + b) = sinacosb + cosasinb) => T1 = (Fgcostheta2) / sin(theta1 + theta2) QED
5 posts
• Page 1 of 1
What was the present that Nate gave Ruby, in the book Lock and Key? What secret to you keep locked inside your dresser drawer? How is it possible that a total-slob college roommate can get his potato-chip crumbs in your sock drawer? Whats a good way to lock my dresser drawers I caught my parents... Will you rate my first chapter, 1-10? thank you? Would you tell me what you think of my chapter 1, please my filing cabinet lock is broken but the bar in the back has the drawers closed. How can I release the bar? Would you read my first chapter and tell me what you think Appropriate ways to discipline your 4 year old How can I remove or break the lock on a steamer trunk? What are my options? Maybe I'm just paranoid . . . I'm bored and home alone Who is onlineUsers browsing this forum: 4 guests |