2- The following massless rigid plate is suspended by 3...

2- The following massless rigid plate is suspended by 3 cables. The geometric and material properties of the cables are presented in the table below. Cable 1 2 3 E (GPa) 200 200 200 A (mm²) A 1.5A 2A 2 3 P q 1 L (mm) 2000 3000 5000 $\sigma_{allow}$(Mpa) 140 140 140 1 1 3 Rigid plate a) If the values of P = 60 KN and q = 6 KN/m are given. Obtain the minimum value of A. b) Obtain the verical deflection at right side of the plate.

Transcript

00:01 In this question we have a pulley.

00:02 So in the first part of the question let us assume that the pulley is frictionless.

00:08 So frictionless means the tension on the both rope will be same is same.

00:17 Then in the second part of the question it is assumed that the pulley is massless.

00:23 So pulley is massless means there will be no moment of inertia acting on the pulley.

00:27 So taking place about the pulley.

00:30 So no moment of inertia about pulley.

00:32 So there will be no extra acceleration.

00:36 No extra acceleration on the rope or by the rope.

00:43 In the third part of the question we are assumed that the rope is inextensible.

00:48 So rope is inextensible.

00:53 Here the force is directly transferred to is directly transferred from one side to another.

01:05 So these are the consequence of the basic assumptions.

01:11 Now in the second part of the question.

01:13 So this is the free body diagram for the given question.

01:17 Now here we can see that here the force or the tension acting on the block a is two times the tension acting on the block b.

01:25 Therefore acceleration on the mass b will be equal to two times the acceleration of the box a.

01:34 Then in the third part of the question we have to find the relationship between tension.

01:39 So which is assumed that the tension on a is two times the tension on b.

01:47 So here we can see that here there is a pulley.

01:53 So which is acting.

01:54 So there is here there is a tension and here there is a tension.

01:58 So the tension on the a is two times the tension acting on the b.

02:02 Then in the third part or in the fourth part we have 2t.

02:07 So by force balancing condition we have 2t minus.

02:11 So this is 2t minus.

02:19 So this is by force balancing condition we have mass into g.

02:24 So that is m into g.

02:26 Then it is balanced by.

02:28 So we have sine of angle theta.

02:31 So sine theta plus the frictional force f.

02:35 So plus f which is equal to the net force is equal to 200 into acceleration a.

02:42 So this can be correctly written as it is 2t minus 200 into g sine theta plus f is equal to 200 into a.

02:55 So here the block is lifted by the block b.

02:59 So the force acting on the block a is given by.

03:03 So now this is the force acting on the block a where we have.

03:08 So initially the block is at rest.

03:11 Therefore acceleration will be equal to zero for block a.

03:17 Therefore we are left with the term...

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