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

Determine the orientation of neutral axis, The resultant moment M acts thro...

The resultant moment M acts through the centroid of the aluminum strut, inclined as shown.  (a) Determine the orientation of the neutral axis and show the neutral axis on a sket

Chemestry cycle 1st yr, Explain construction and working of calomel electro...

Explain construction and working of calomel electrode

Compute the maximum efficiency of the solar cell, The main objective is to ...

The main objective is to compute the maximum efficiency of the solar cell panels, produce hydrogen and estimate the hydrogen production rate using solar cells and electrolyzer and

Cam, advanced cam profile synthesis

advanced cam profile synthesis

Seasonal-component analysis, Seasonal-Component Analysis: A food proce...

Seasonal-Component Analysis: A food processor uses a moving average to forecast next month's demand. Actual demand data for the past few months is available as depicted in the

Basis of evaluation entrepreneurship development, The following form basis ...

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

Define the gear hobbing, Define the Gear Hobbing This is the most produ...

Define the Gear Hobbing This is the most productive of all the gear production processes. However, it can only be used for producing spur gears and worn gears. It cannot be use

Postweld heat treatment, Q. Postweld heat treatment? When the equipment...

Q. Postweld heat treatment? When the equipment data sheet specifies post-weld heat treatment either for service conditions or code requirements, welding, hammering (peening), o

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