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
In general safety and service tips, you learnt about general service and safety tips those must be followed while working in workshop. It gives the competency statements useful for

Using Bode plot calculate (a) Phase margin (b) Gain margin (c) Stability of closed loop system. The open transfer function of the system is

(Buoyancy; force & moment balance) A partially submerged, homogeneous timber is 0.15m by 0.35m in cross-section. What is the specific weight of the timber and the tension in the r

Pin-jointed steel structure: Find out the forces in the members of the pin-jointed steel structure. Solution Joint D  Suppose f CD and f DE both as tensile forc

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

For a transfer function graph with h(t) on the y-axis and time in seconds on the x-axis, the h(t)=1 from 0 to 2 seconds, while h(t)=0 everywhere else. How do I graph the unit step

steel ball v/s cotton ball of same weigt which is easy to lift

round reamer diagram

a plano concave lens is used instead of plano convex lens in newtons ring

aframe of punching machine and its varios dimentions. if it has force of85kN determine others