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
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

Derive mathematical equation for the time response of a first order system subjected to ramp input. Draw the response curve and determine steady state error. Give some examples of

Explain the Base of radial drilling machine The base of the drilling machine handles the entire machine and when bolted to the floor, gives for vibration-free operation and bes

why single point cutting tool used in lathe

Q. Design lay-down areas for plant? Designated lay-down areas are areas specifically positioned to enable equipment maintenance to be carried out. These are normally assigned f

example on operation sheet?

Requiremen t of Temperature Scale: The temperature scale on which temperature of the system can be read is required to assign the numerical values to the thermal state of the

A load cell based on a "proving ring" is shown below.  The circular portion of the load cell has an inner radius of 1.25 in and outer radius of 1.50 in.  The ring has a depth (i.e.

Illustration of CAM A cam rotating at consisted angular velocity operates an oscillating follower. Draw cam profile for the given data: Angular displacement of the follower

Q. Show Conceptual Layout of plant ? During the Evaluate phase of a project, the early concept design considers broad information of the expected installation, and its basic cr