Evaluate the acceleration of the three weights, Mechanical Engineering

Evaluate the acceleration of the three weights:

A system of weight connected by the string passing over pulleys A and B is shown in figure given below. Find out acceleration of the three weights. Assume the weightless string and ideal condition for the pulleys.

Sol: As strings are weightless and ideal conditions prevail, thus the tensions in string passing over pulley A will be same. The tensions in string passing over pulley B will be same. But tensions in the strings passing over pulley A and over pulley B will be different as shown in the given figure.

Let T1  = Tension in string passing over pulley A
T2  = Tension in string passing over pulley B

One end of string passing over pulley A is connected to the weight 15N, and other end is connected to pulley B. As weight 15N is more than weights (6 + 4 = 10N), thus weight 15N will move downwards, while pulley B will move upwards. The acceleration of weight 15N and of pulley B will be same.

Let, a  = Acceleration of block 15N in the downward direction1  = Acceleration of 6N downward with respect to the pulley B.

Then acceleration of weight 4N with respect to the pulley B = a1  in upward direction.

1385_Evaluate the acceleration of the three weights.png

The absolute acceleration of weight 4N,

= Acceleration of 4N with respect pulley B + Acceleration of pulley B. = a1 + a (upward)

(as both the acceleration are in upward direction, total acceleration will be the sum of the two accelerations)

Absolute acceleration of weight 6N,

= Acceleration of 6 with respect to pulley B + Acceleration of pulley B.

= a1 - a (downward)

(As a1 is acting downward while a is acting upward. Thus total acceleration in downward direction)

Consider motion of weight 15N Net downward force = 15 - T1

Using F = ma,

15 - T1 = (15/9.81)a                                                                                                                         ...(1)

Consider motion of weight 4N

Net downward force = T2  - 4

Using F = ma,

T2  - 4 = (4/9.81)(a + a1)                                                                                                               ...(2)

Consider the motion of weight 6N

Net downward force = 6 - T2

Using F = ma,

6 - T2 = (6/9.81)(a1 - a)                                                                                                                ...(3)

Consider motion of pulley B,

T1=2T2                                                                                                                                         ...(4)

Adding equation (2) and (3)

2 = (4/9.81)(a + a1) + (6/9.81)(a1 - a)

9.81 = 5a1 - a                                                                                                                               ...(5)

Multiply equation (2) by 2 and put value of equation (4),

T1  - 8 = (8/9.81)(a1  + a)                                                                                                                ...(6)

Add equation (1) and (6), we get

15 - 8 = (15/9.81)a + (8/9.81)(a1  + a)

23a + 8a1 = 7 X 9.81                                                                                                                           ...(7)

Multiply equation (5) by 23 and add with equation (7),

a1 = 2.39m/sec2                                                                                                                         .....ANS

Putting value of a1 in equation (5),

a = 2.15m/sec2                                                                                                                            ....ANS

Acceleration of weight 15N = a = 2.15m/sec2                                                                   ......ANS

Acceleration of weight 6N = a = 0.24m/sec2                                                                     .......ANS

Accelerationofweight  4N = a = 4.54m/sec2                                                                      .......ANS


Posted Date: 10/20/2012 12:47:51 AM | Location : United States







Related Discussions:- Evaluate the acceleration of the three weights, Assignment Help, Ask Question on Evaluate the acceleration of the three weights, Get Answer, Expert's Help, Evaluate the acceleration of the three weights Discussions

Write discussion on Evaluate the acceleration of the three weights
Your posts are moderated
Related Questions
Q. Scraper Launchers and Receivers? Scraper launchers and receivers associated with the pipelines shall be located in open, well-ventilated areas with the opening directed away

Difference between direct and shear stress

Q. Show Prevailing wind conditions for plant layout? Prevailing wind conditions influence the design considerations for the location of the flare or vent stack. It is vital tha


What do you mean by sensitivity in a governor?

Advantage of Electro Chemical Machining 1. As the tool does not come in contact with the work there for tool wear is practically nil. 2. The metal removal is faster rate.

Define Essentials of Milling Fixture? Strength of withstand heavy forces. Thrust should be directed towards a strong, solid structure. Cutter setting piece should b

GAS METAL ARC WELDING-PRINCIPLE OF OPERATION Gas Metal Arc Welding (GMAW) is one of the arc welding processes in which an electric arc is formed and maintained between a continuo

Seawater is boiled in a 5 liter kettle to produce drinking water.  In class we solved the steady-state version of this problem.  Here you are asked to consider the transient period

Q. What is Crest gauges explain? In case of bridges, it is sometimes necessary to observe high flood levels rather than daily gauges to ensure that minimum clearance is not enc