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
USAGE OF SPECIAL TOOL: The common tools used in repair and maintenance of motorcycles were introduced to you in previous sections. Now, we shall learn about some special tools and

GENERAL FACTORS BEHIND ACCIDENT:  Following are the factors, which may cause accidents in workshop, so we should take care of these factors: Insufficient light and ventilati

Ask question #MiThe steam that leaves the super-heater is expanded from 130bar at 535°C to 25.2bar at 310°C in a high pressure turbine. The steam from the exit of the HP turbine is

Coplanar and Non-Coplanar Forces: In this unit, you have learnt to identify the different systems of forces. You have also learnt the many techniques of adding the forces to g

(a) What is the importance of safety at workshop? (b) What problems may arise, if we do not take safety precautions in the workshop?

(a) What will happen if air filter is not used? (b) What are the components of an air filter? (c) What precautions should be followed while cleaning the air filter? (d) What grade

Determine the maximum uniformly distributed load: A timber beam 150 mm wide & 300 mm deep is supported simply over a span of 4 m. determine the maximum uniformly distribute

Manufacturing DATABASE system in FMS

Determine the Excavation of soil Excavation of soil in open well foundations is done  by dredging with grab buckets or similar equipment. The volume of excavated soil always e

The following form basis of evaluation : The unit has obtained all necessary clearances whether statutory or administrative, e.g. drug license under drug control order, NOC