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

Explain arc-welding processes, Arc-Welding Processes Arc-welding incl...

Arc-Welding Processes Arc-welding includes those welding processes wherein heat required for welding is derived from an arc powered by electrical energy, may be AC of DC as s

Parts of wilson hartnell governor, what are the parts of wilson hartnell go...

what are the parts of wilson hartnell governor with their designation?

Define what is nose radius, Define What is Nose Radius? The nose radius...

Define What is Nose Radius? The nose radius is provided to increase finish and strength of the cutting tip of the tool. Small radii will produce smooth finish and are used on t

Various components of transmission system , Various Components of Transmiss...

Various Components of Transmission System Primary Drive Gear : It is mounted on crankshaft. It transfers power to primary driven gear. Primary Driven Gear : It is

What is mapp gas welding, Q. What is MAPP Gas Welding? Methyl acetylene...

Q. What is MAPP Gas Welding? Methyl acetylene-propadiene-petroleum (M inert than other gas mixtures, making it safer for use and store. MAPP can also be used at very h high-vol

Illustrate the design process and application of cad, Describe the use of c...

Describe the use of computer in : (i) Design (ii) Manufacturing Illustrate the design process and application of CAD.

Explain the meaning of a raft foundation, Explain the meaning of A raft fou...

Explain the meaning of A raft foundation A raft foundation, as also combined footing, cannot be considered to be the opposite of a slab supported on the columns with a defined

Wedge problems, How to solve wedge problems..can anyone just explain the me...

How to solve wedge problems..can anyone just explain the method..

Basic concept of servicing and maintenance, Basic Concep: Proper care and ...

Basic Concep: Proper care and maintenance are essential for trouble free operation and optimum performance of the motorcycle. A quality service at regular intervals ensures that e

Concentrated or point load on beam, Concentrate d or Point Load: Ho...

Concentrate d or Point Load: How many types of load are acting on the beam? A beam is usually horizontal and the loads acting on beams are usually vertical. The followi

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