Determine acceleration of weight, Mechanical Engineering

Assignment Help:

Determine acceleration of weight:

Two pulleys of radii 200 mm and 400 mm are mounted co-axially and rigidly on a common-shaft.

These pulleys have a overall mass of 28 kg and radius of gyration of 200 mm of the combination. If weights W1 = 40 N and W2 = 50 N are suspended from points A1 and A2 by ropes which are wound round the two pulleys, determine acceleration of weight W2. Suppose g = 10 m/sec2.

Solution

 Clockwise moment of W1 about centre of pulley

= 40 × 0.4 = 16 N.m.

Anticlockwise moment of W2 about centre of pulley = 10 N.m.

Therefore the pulley shall rotate clockwise with angular acceleration α about the centre. After some time, W2 shall have moved a distance s2 with acceleration a2 and shall have velocity of v2  = r2  ω , while W1 will move

Distance  s1 = 2 s2  = 2 r2  θ .

with final velocity V1 = r1  ω = 2 V2

with acceleration .a1 = r1  α = 2 a2

Since,   rk  = 0.2 m.

I (m) = 28 × (0.2)2       = 1.12 kg m2

ω2 = 2 × α θ

By Using Principle of Conservation of Energy, and letting datum level as (A - A),

1561_Determine acceleration of weight.png

40 (s1 ) + 50 (so) = 50 (s1/2)  + 50 (so) + (40/10) × (V1)2 /2+ 50 × (V2)2 /2+( Im ω2 )/2

40 (s ) - 25 s = ω2 [2  × (0.4)2 + 2.5 × (0.2 )2 +(1.12/2)]

15 × (0.4 θ) = 2 α θ [0.32 + 0.1 + 0.56]

∴ α = 3.06 rad / sec 2

α ≈ 3 rad / sec 2 .


Related Discussions:- Determine acceleration of weight

What is the velocity of the crosshead - crank, What is the velocity of the ...

What is the velocity of the crosshead - crank: In the slider crank mechanism shown in Figure, the crank is rotating clockwise at 120 revolution/minute. What is the velocity of

Classification-plastics-reinforced plastics and adhesives, Classification ...

Classification Two categories of plastics are identified. Those are: thermosetting plastics and thermoplastics. Plastics generally cannot stand higher temperatures. They becom

Expression for strain energy, Expression for strain energy: Derive an...

Expression for strain energy: Derive an expression for strain energy because of torsion.                                          Sol.: The work done in straining shaf

Heat transfer and temperature distribution, Derive the mathematical express...

Derive the mathematical expression for heat transfer and temperature distribution through infinite long fin?

Calculate the maximum bending moment, A shaft is supported on bearings A an...

A shaft is supported on bearings A and B, 800 mm between centres. A 20° straight tooth spur gear having 600 mm pitch diameter, is located 200 mm to the right of the left hand beari

Equation of motion of lift, Equation of motion of lift: Write equatio...

Equation of motion of lift: Write equation of motion of lift when move up and when move down   Assume,   W = Weight carried by lift m = Mass carried by lift = W

Welding procedure and performance qualification, WELDING PROCEDURE AND PERF...

WELDING PROCEDURE AND PERFORMANCE QUALIFICATION A total quality assurance scheme, embracing all aspects of manufacture would have necessarily made all attempts to ensure

What is wrap-around, The major purpose of a wrap-a-round is to make a strai...

The major purpose of a wrap-a-round is to make a straight line around a pipe to aid in cutting the pipe to its proper length. It is used mainly as a template or a straight edge.

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