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.

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.

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

Generation of steam at constant pressure: Steam is pure substance. Like any other pure substance it can also be converted into any of the three states, that is, solid, liquid

(a) Can you explain limitations of Euler's theory (b) Derive a mathematical expression to determine the crippling load of a column with on end fixed and other end hinged (c)

I have 5000 kg boiler capacity. In flow of 1 m3 gas flow how much steam I can produce

Rubber Rubber is a plastic that is largely derived from natural sources and utilized in a modified form. For automobile tyres, Rubber is well identified as material. Rubber re

Q. A beam made of C.I. having section of 50mm external diameter and 25 mm internal diameter is supported at 2 points 4 m apart. The beam carries concentrated load of 100N at the ce

Quasi static process - thermodynamics: Thermodynamic equilibrium of a system is very difficult to be realized during the occurrence of a thermodynamic process. 'Quasi-static'

Examine the CNC machines at University of Greenwich. You are needed to present and discuss about the major functional units and vital machine elements of  the CNC milling at Univer

Plate oil Separator: Check for plate oil separator fitment.

Q. What is Bolt Elongation? The required bolt elongation Δ 1 may be calculated by the equation (7): Δ 1 = 3.25 * 10-8 * SB * L0 (in) (7) Where L 0 is the effect