Calculate the angular acceleration of the pulleys, Mechanical Engineering

Calculate the angular acceleration of the pulleys:

The compound pulley system has a mass of 30 kg and a radius of gyration of 450 mm. Calculate the tension in each cord and the angular acceleration of the pulleys when the masses are released (Refer following Figure).

1648_angular acceleration of the pulleys.jpg

Solution

Free body diagram for the pulley and both the masses are drawn separately as shown in the figure.

We must keep in mind that a1 = 0.6 α and a2 = 0.3 α acceleration (i.e. difference in radii). where α is the angular

 Inertial forces are illustrated on FBD. Now, we may write down dynamic equilibrium equations for each of the body.

For a mass of 50 kg, we have

∑ Fy  = 0                     ∴ T1 - 50 a1 - 50 × 9.81 = 0

Substituting for a1 in terms of α, we get

T1  = 50 × 0.6 α + 50 × 9.81

= 490.5 + 30 α  ------------- (1)

For the mass of 150 kg, we have

∑ Fy  = 0                  ∴ T2  + 150 . a2  - 150 × 9.81 = 0

∴ T2  = 1471.5 - 150 × 0.3 α

= 1471.5 - 45 α             ---------- (2)   

For the pulley, we have ∑ M  = 0

∴ 0.6 T1  + I α - 0.3 T2  = 0

But       I = 30 × (0.45)2  = 6.08 kg m 2

∴ 0.6 T1  - 0.3 T2  = - 6.08 α                  ---------- (3)

Solving Eqs. (1), (2) and (3) as below, we obtain

0.6 T1  - 0.3 T2  = - 6.08 α

0.6 (490.5 + 30 α) - 0.3 (1471.5 - 45 α) = - 6.08 α

or,        147.15 = 37.58 α

α = 3.91 rad / sec.

Substituting this value of α in Eq. (1) and (2) above we obtain

T1  = 607.8 N

and T2  = 1295.55 N.

Posted Date: 1/29/2013 6:36:25 AM | Location : United States







Related Discussions:- Calculate the angular acceleration of the pulleys, Assignment Help, Ask Question on Calculate the angular acceleration of the pulleys, Get Answer, Expert's Help, Calculate the angular acceleration of the pulleys Discussions

Write discussion on Calculate the angular acceleration of the pulleys
Your posts are moderated
Related Questions
Q. What is Passive Fire Protection? Passive fire protection is defined as any fire protection system that, by its nature, plays an inactive role in protecting personnel and pro

Equilibrium of body - force acted at any angle: Magnitude of force ' p ' which is required to move the body down the plane. When ' p ' is acted with an angle of φ.

Isolated and Combined Footings Individual columns are generally supported on isolated footings. A typical isolated footing is shown in Figure. This arrangement is suitable when

Q. Firing Rate Demand for Steam Generator? The firing rate for each Steam Generator is proportional to the feedwater flowing into that Steam Generator. Thus, the sum of the pa


Q.  The area of the hysteresis loop of a given magnetic material is 50cm 2 with the two axes scaled as 1cm = 20AT and 1cm = 50mWb, for 50Hz frequency find the total hysteresis

Evaluate velocity of the block: A block of 2500N rest on horizontal surface. The coefficient of friction in between block and plane is 0.3. The block can be pulled by the for

opitz system in group technology

Course content on design, CAD modeling, linkage synthesis, and creating proper engineering drawings is the focus for this project. In terms of design, a logical starting point wou

Calculate the tension T in the rope: Q: A man raises 10 Kg joist of length 4m by pulling on rope, Find out the tension T in the rope and reaction at point A for the posit