Evaluate the motion of the system, Mechanical Engineering

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.


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.

Posted Date: 1/29/2013 7:14:42 AM | Location : United States

Related Discussions:- Evaluate the motion of the system, Assignment Help, Ask Question on Evaluate the motion of the system, Get Answer, Expert's Help, Evaluate the motion of the system Discussions

Write discussion on Evaluate the motion of the system
Your posts are moderated
Related Questions
A number of heavy items are to be off-loaded from a Heavy-Lift Ship and placed on a series of "support assemblies" on the quayside to await transportation by road to their destinat

Inventor claims in adiabatic system: On e inventor claims that 2 kg of air supplied to magic tube at 4 bar and 20°C and the two equal mass streams at 1 bar are produced, one

Determine the force to pull box along a level surface: A metal box having weight 10KN is pulled along a level surface at the uniform speed by applying horizontal force of 350

Q. Describe about consumable electrode? This type of electrode is prepared from metal. Its one end is kept in electrode holder and then electric supply is passed through it. Th

Clearly indicate fire dampers on ducts penetrating fire rated partitions, equipment rooms, duct shafts, ceiling outlets, etc. Detail fire dampers on drawings if required. For

Airport Drainage: Rainwater should be quickly taken away from the runway, taxiway and apron areas. For drainage of runway and taxiway, a cross-slope of 1.5 per cent on either

Explain POINT ANGLE - Angle of drills It is also known as a cutting angle. Its most commonly used value for a large variety of materials is 118.Though,its varies from 80 to 140

Two kg Ammonia (mA) at PA = 300 kPa and TA = -10ºC and 1 kg Ammonia (mB) at PB = 300 kPa and TB = 100ºC are mixed in a constant pressure and adiabatic process. Find the following:

what are the threats of mechanical engineering ?

derivation for varing shear stress for thin circular tubes.