Determine the acceleration of each block, Mechanical Engineering

Assignment Help:

Determine the acceleration of each block:

In the system of associated blocks shown in figure the coefficient of kinetic friction under blocks A and C is 0.20. Determine the acceleration of each block and the tension in the connecting cable. The pulleys are assumed to be frictionless and of negligible weight.

 Preliminary Discussion

For simplification, we resolve the weights of A and C into their components acting parallel and perpendicular to the inclined planes, as shown in the free body diagrams. First thing, we must try is to determine the direction of motion of the system. We first suppose that one part of the system does not move and then calculate the tensions necessary to keep it at rest. We then calculate the forces in the remaining system and if any unbalanced force is obtained that part will move in the direction of the force. Also, we take into account the influence of friction in preventing the motion.

In this case, let us assume that block B is at rest. This gives us 2 T = 1200 N or T = 600 N acting at A and C.

If we substitute T = 600 N and sum up the forces parallel to the plane, then frictional force required for equilibrium is 800 - 600 = 200 N, but available friction force on A is 120 N. This is insufficient to keep A at rest and as shown, A shall be moving down the plane. Similarly, block C will move upwards as shown.

Yet we do not know the direction of motion of B because down plane motion of A will tend to raise B upwards whereas up plane motion of C will tend to lower down B. We now assume that let B move downwards as no frictional force is acting on B and incorrect direction of motion will be only importance. The actual value of T will determine its motion.

Now, let us remember the FBDs of A and C. For downward motion of A, T must be less than 800 - 120 = 680 N and for upward motion of C, T should be more than 320 + 48 = 368 N. Thus, we may estimate the value of T as average of (680 + 368) /2 = 524 N.

By using this approximate value of T on FBD of B gives an unbalanced downward force on B and justifies our assumption that B moves down.

We now try to use the concept of method of virtual work to get the kinematic relationships. The entire work done by internal associating forces on a system is zero.

We also keep in mind that work is a product of force and displacement and positive work is done when the displacement is in the direction of force. We have sum of the works done by T on the system of connected blocks.

                                          TSC  - TS A  - 2 TS B  = 0

By cancelling T, we get

SC  = S A  + 2 S B                -------- (a)

∴  vC  = v A  + 2 vB               ------------ (b)

    And  aC  = a A  + 2 aB                 ---------- (c)

Solution

Now we apply equilibrium equations to each body.

For A            800 - 120 - T - (1000/g) aA   = 0                      ---------- (1)

For B                 1200 - 2 T - (1200/ g) aB   = 0                      ---------- (2)

For C                T - 48 - 320 - (400/ g) aC      = 0                 ------------- (3)

We replace ac by a A  + 2 aB . We obtain

T + 101.94 a A  = 680

2 T + 122.324 aB  = 1200

T - 40.77 aA  - 81.55 aB  = 368

∴ a A   =           680 /101.94     - T /101.94

And     aB  =      (1200 /122.324)  -      (2 T /122.324)

T - 40.78 [ (680/101.94) - (T/101.94)]  - 81.55 [(1200/122.32)  -(2 T/122.324)]    = 368

∴ T + 0.4 T - 272.027 + 1.33 T - 800.103 = 368

2.73 T = 1440.13

T = 527.52 N

Substituting these values in Eq. (1) etc., we obtain a A = 1.496 m / sec2 aB = 1.185 m / sec2

aC  = 3.912 m/sec2


Related Discussions:- Determine the acceleration of each block

Calculate the normal time for this operation, a) Describe Industrial Engine...

a) Describe Industrial Engineering. Discuss its scope and use in service and manufacturing industries. b) Deriving the stop watch study in a machine shop, ten observation of a d

Head loss, calculate the head required

calculate the head required

Engine, maximum rpm at engine

maximum rpm at engine

Internal combustion engines, During a test on a Lister engine in a thermal ...

During a test on a Lister engine in a thermal laboratory, following parameters were measured; crank shaft speed=1,750rpm Load on dynamometer=220N Radius of dynamometer=1.5m Fuel co

Evaluate hydraulic efficiency, A pelton wheel works at the foot of a dam be...

A pelton wheel works at the foot of a dam because of which the head available at the nozzle is 400m. The nozzle diameter is 160mm and the coefficient of velocity is 0.98. The diame

Cam, advanced cam profile synthesis

advanced cam profile synthesis

What is epoxy powder, Q. What is Epoxy Powder? The coating manufacturer...

Q. What is Epoxy Powder? The coating manufacturer shall be consulted as to the product best suited to the Applicator's speed of coating, pipe diameter and wall thickness, and t

Acceleration of the two blocks, In the drawing, the weight of the block on ...

In the drawing, the weight of the block on the table is 380 N and that of the hanging block is 215 N. Ignore all frictional effects, and assuming the pulley to be massless.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd