Sample Problem 1. An engine with weight w hangs from a chain that is linked at apoint O to two other chains, one is connected to the ceiling and the other one to thewall. Find the tension in each of the three chains, assuming that w is given and theweights of the chains are negligible.Fren tyagram of ergine h m of ring OFre totySolution:Ti is equal to weight w. The horizontal and slanted chains don't exertforces on the engine itself but they are connected on the ring where the threechains join. The weight of the ring itself is negligible.T, Ta, and Ty are the magnitudes of the forces while their directions areshown in the free-body diagram. Take note that the downward force withmagnitude Ti of the chain acting on the engine are not an action-reaction pair.Using the x and y-components, we find thatEFx 0, Ta cos 70 + (-Ta)-0EF,-0, Ts sin 70' + (-T)-0Because T-w, we can rewrite the second equation as:T3-T1/sin 70- w/ sin 70-0.940wWe can now use this equation in the first equation:T-Ts cos 70'-(0.940w) cos 70'-0.321w.Now, we can express all the three tensions as:Ti-w; T-0.321w; T3.940wIf the engine is weighing 3000 N, then,T 3000 NT (0.321) (3000 N)-965 NT (,940) (3000 N)-2819 NSample Problem 2. An object with a certain mass mi moves in a frictionless track.It is connected by a string passing through a frictionless pulley to a hanging to aweight with mass ma. The string doesn't stretch. Find the acceleration of eachobject and the tension in the string.Febdygram r gram hr hFreetySOLUTION:

Answered: Image /qna-images/answer/b5e0fc59-1577-4cd4-a36e-676c44e6f19d.jpg

Sample Problem 2. An object with a certain mass m: moves in a frictionless track. It is connected by a string passing through a frictionless pulley to a hanging to a weight with mass ma. The string doesn't stretch. Find the acceleration of each object and the tension in the string. Aperatn

Sample Problem 2. An object with a certain mass m: moves in a frictionless track. It is connected by a string passing through a frictionless pulley to a hanging to a weight with mass ma. The string doesn't stretch. Find the acceleration of each object and the tension in the string. Aperatn

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

Sample Problem 1. An engine with weight w hangs from a chain that is linked at a
point O to two other chains, one is connected to the ceiling and the other one to the
wall. Find the tension in each of the three chains, assuming that w is given and the
weights of the chains are negligible.
Fren ty
agram of ergine h m of ring O
Fre toty
Solution:
Ti is equal to weight w. The horizontal and slanted chains don't exert
forces on the engine itself but they are connected on the ring where the three
chains join. The weight of the ring itself is negligible.
T, Ta, and Ty are the magnitudes of the forces while their directions are
shown in the free-body diagram. Take note that the downward force with
magnitude Ti of the chain acting on the engine are not an action-reaction pair.
Using the x and y-components, we find that
EFx 0, Ta cos 70 + (-Ta)-0
EF,-0, Ts sin 70' + (-T)-0
Because T-w, we can rewrite the second equation as:
T3-T1/sin 70- w/ sin 70-0.940w
We can now use this equation in the first equation:
T-Ts cos 70'-(0.940w) cos 70'-0.321w.
Now, we can express all the three tensions as:
Ti-w; T-0.321w; T3.940w
If the engine is weighing 3000 N, then,
T 3000 N
T (0.321) (3000 N)-965 N
T (,940) (3000 N)-2819 N
Sample Problem 2. An object with a certain mass mi moves in a frictionless track.
It is connected by a string passing through a frictionless pulley to a hanging to a
weight with mass ma. The string doesn't stretch. Find the acceleration of each
object and the tension in the string.
Febdy
gram r gram hr h
Freety
SOLUTION:

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