Find out the velocity of the system, Mechanical Engineering

Find out the velocity of the system:

Blocks A and B of mass 20 kg and 45 kg, respectively are associated by a weightless rope over a frictionless pulley as shown in Figure a). Suppose a coefficient of friction of 0.2 for all the planes. Find out the velocity of the system 5 seconds after starting from rest.

524_Find out tension in the rop.jpg

Solution

Consider T be the tension in the strings. This is not rather easy to determine the direction of motion. Let us suppose that block B is moving down the plane such that block A climbs up the plane. It gives us the direction of acceleration for each of block and also the directions of frictional forces acting on each block.

Refer Figures (b) and (c). These figures give us free-body diagram for each block.

Consider Block A

We may write the following equilibrium equations. Supposing x axis along the plane and y axis perpendicular to the plane.

∑ Fx  = 0,                   ∴ T = 20 a + 0.2 N1  + 20 g sin 30o                 ---------- (1)

∑ Fy  = 0,                     N1 = 20 g cos 30o = 169.91 N                     ------------ (2)

By Substituting in (1), we obtain

T = 20 a + 132.08                   -------- (3)

Consider Block B

Now we may writer equilibrium equations for this block.

∑ Fx  = 0,          T + 0.2 N 2  + 45 a = 45 g sin 60o           --------- (4)

∑ Fy  = 0,                N 2  = 45 g cos 60o

                                        = 220.72 N                ----------- (5)

 By Substituting in (4), we obtain

T + 44.145 + 45 a = 382.30

∴ T + 45 a = 338.155                     --------- (6)

 Solving Eq. (3) and Eq. (6), we obtain

T = 20 a + 132.08 = - 45 a + 338.155

∴ 65 a = 206.07

∴ a = 3.17 m / sec2.

The value of a, we have attained is positive and our supposition that block B moves down the plane is correct.

We can now apply kinematic equation,

v = vo  + a t                   ∴ v = 0 + 3.17 × 5

                                     = 15.85 m / sec 2.

Posted Date: 1/29/2013 2:25:56 AM | Location : United States







Related Discussions:- Find out the velocity of the system, Assignment Help, Ask Question on Find out the velocity of the system, Get Answer, Expert's Help, Find out the velocity of the system Discussions

Write discussion on Find out the velocity of the system
Your posts are moderated
Related Questions
calculate wavelength fpr monocromatic light using newtons ring experiment notes

A jet of water moving at 8 m/sec. impinges on a concave-shaped vane to deflect the jet through 120 o when stationary. If the vane is moving at 5 m/sec., calculate the angle of jet

Lubrication Complaints If the engine oil level is too low, check for the following things: External oil leaks Worn out piston rings Worn out valve guide and/o

Determine the change in diameter: A thin spherical shell of 1.8 m diameter is 10 mm thick. This is filled with a liquid so that the internal pressure is 1 N/mm 2 . Determine t

Define the difference modes of Heat Transfer with examples. State one system where Heat Transfer takes place because of all modes of Heat Transfer.



Hi ... I have a final project I need to finish it soon about 3 weeks from now ... to design any machine by the Solidworks program .... please feed me back if you can .. thank you

temparature stresses in composite bars

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