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
The first stage of design assumes: budget is approved, marketing research is complete, product can be made at a price below that which it can be sold, research and development is c

TYPES OF ELECTRON BEAM WELDING GUN   Diode (Cathode - anode) Gun : In this gun, the beam shaping electrode and the emitter are both at the same electrical potentials. These

State about the Computer-aided design Computer-aided design (CAD), high-quality character fonts, data plots, and artists' sketches all contain smooth curves and surfaces. The pa

Problem specification 5 kg of air is contained in a piston-cylinder device, initially at a pressure of 2MPa and a specific volume of 0.08m3/kg. The air then expands, as an ideal ga

a) The total estimated time for an operation ie assembly of a pin is 2 minutes. If the rating is 120% determine normal time. If total allowances allowed are 10% for that job, calcu

how degree of super heat reduces specific steam consumption

Q. Determine the proper torque values from the Flange? Determine the proper torque values from the Flange Closure Sheet. Apply the torque, using a hand torque-measuring wrench,

SUBMERGED ARC WELDING-Set Up Submerged arc welding system consists of the following basic modules: 1. Welding head 2. Power source 3. Flux feeding and recovery units Schematic

What is tetra & octahedral voids & how are they formed ?

A motor cycle with its rider, weight 250kg, the centre of gravity of the machine and rider combined being 60cm above the ground level when the machine is standing upright. Each roa