Evaluate the motion of the system, Mechanical Engineering

Assignment Help:

Evaluate the motion of the system:

If in above Example, the block A is resting on an inclined plane at 45o to horizontal as illustrative in Figure, find out the motion of the system assuming μ = 0.1.

Solution

Supposing that block A moves upwards a distance s while B moves downwards by (s/2) as before as shown in Figure

N A  = WA  cos 45o

= 400 × 0.707

= 283 N.

Friction = 0.1 × 283

By using the principle of conservation of energy & letting datum level as B′ which is the final position of B,

W (H + (s/2))+ WB× (s/2) = WA ( H + (s /2)+ s × sin α + (1/2)M A  V 2  +(1/2)MB (V/2)2 + 28 × s

∴ 10 × g ( s/2)   - 40 × 0.707 s - 28 × s = V 2  (40 +(10/4))

By using equation of motion of uniform acceleration a,

                  V 2 = 2 a s   (since initial velocity is zero)

∴ approximately   49 - 28 - 28 = a (42.5)

 ∴ a = - 7 /42.5 m / sec2

Negative sign indicates that assumed direction of motion of A is not right and therefore the block A moves downward. As direction of friction also changes (that means upwards), the magnitude of acceleration is recomputed separately.

1749_Evaluate the motion of the system.png

The system while A moves down through distance s, its  velocity is V while Block B moves up with velocity (V/2) considering initial- position of Block B as datum level,

                                        V 2 = 2 (a × s)

Where,            a = acceleration of A,

WA (H) = W [H - s (sin α)] + WB (s/2) + 40(V2/2)         + (10/2) (V2/4) + F × s

∴ 0 = - 40 × (s × 0.707) × 9.8 + 10 × (9.8 × s)/2 + (V2 /2) (42.5) + 28 s

∴ 0 = s [(- 280 + 49 + 28) + a × 42.5]

Taking 277.14 ≈ 280

 ∴ a = 203 /42.5

≈ 4.7 m / sec2.

Hence, Block A moves down with acceleration of 4.7 m/sec2.


Related Discussions:- Evaluate the motion of the system

Describe direct extrusion, Q. Describe Direct extrusion? • Direct extru...

Q. Describe Direct extrusion? • Direct extrusion, also known as forward extrusion, is the most common extrusion process. • It works by placing the billet in a heavy walle

Short-term scheduling and control, Short-Term Scheduling And Control Th...

Short-Term Scheduling And Control The major objective at this stage is to make sure the efficient and smooth operation of the system in the event of unforeseen disturbances. Th

Combustion chamber and radiant section, Q. Combustion Chamber and Radiant S...

Q. Combustion Chamber and Radiant Section? The combustion chamber and the radiant heat transfer section of the Steam Generators shall be a horizontal, multiple pass arrangement

Specifications of hardness testing machines and indentors, Specification s...

Specification s of Hardness Testing Machines and Indentors: The Brinel cum Rockwell Tester has specifications which are stated below: Ability to determine the hardness up t

Describe about carbon steel, Q. Describe about Carbon Steel? Steel havi...

Q. Describe about Carbon Steel? Steel having no specified minimum quantity for any alloying element (other than commonly accepted amounts of manganese, silicon, and copper) and

Heavy traffic areas in pumps, Q. Heavy traffic areas in pumps? These ar...

Q. Heavy traffic areas in pumps? These are areas around pumps, filters, control valves, PSV's and other equipment requiring frequent maintenance or servicing. Piping attache

Product Design and Development, I need a work to be done in the field of te...

I need a work to be done in the field of technical function generation for a product development process and about 3000-3500 words on any theoretical topic related to product devel

Determine the width and depth of the beam, Determine the width and depth of...

Determine the width and depth of the beam: A timber beam of rectangular section is only supported over a span of 5 m. It carries an uniformly distributed load of 15 kN/m over

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