Determine acceleration of weight, Mechanical Engineering

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 .

Posted Date: 1/29/2013 7:20:54 AM | Location : United States







Related Discussions:- Determine acceleration of weight, Assignment Help, Ask Question on Determine acceleration of weight, Get Answer, Expert's Help, Determine acceleration of weight Discussions

Write discussion on Determine acceleration of weight
Your posts are moderated
Related Questions
Working Chamber of EBW The chamber is usually rectangular in shape and has heavy windows to permit viewing the work. Both high voltage machines and low voltage machines

describe about pendulum pump mechanism and diagram

Q. Design pressure of Vessels? The design pressure shall be as specified on the Vessel Data Sheet. The design pressure for a vessel in vacuum service shall be full vacuum (1

can we use electrical power chuck for job clamping in cnc lathe.what are the issues related

What is Spot welding equipment? Spot welding machines may by classified as follows on the basis of mechanical Construction; 1. Rocker-arm Machines 2. Press-type machin

I am trying to find out how a hunting scope is manufactured with proper steps and what machines are used to make a scope?

A biaxial rosette is shown at right. Derive equations to correct for transverse sensitivity effects for the case in which the two strain gage elements exhibit different gage factor

Q. Explain caustic Stress Corrosion Cracking? Dilution of the caustic prior to injection into a relatively hot stream will minimize the potential of caustic Stress Corrosion Cr

Slip of belt: Sol:   When the driver pulley rotates, it carries belt, because of a firm grip between its surface and belt. The firm between pulley and belt can be obtained by

A steel plate with dimension shown in sketch (a) below is subjected to P = 150 kN tensile force and M= 300 N-m bending moment. The plate is made of AISI 1080 steel. A hole is to be