Determine the tension in the cord, Mechanical Engineering

Determine the tension in the cord:

Two blocks containing the weights and positions illustrated in Figure rest on a frame which rotates around its vertical axis at a constant speed. The coefficient of friction among the blocks and the frame is 0.20 neglecting the weight and the friction of the pulley. Compute the speed in rpm at which the blocks shall start to slide. Also determine the tension in the cord at that instant.


As the system starts rotating around the vertical axis, acceleration equal to r ω2 will be acting on each block. The outer block shall have magnitude of acceleration more and has a mass larger than the other block. Thus, we will assume that outer block will have a motion oriented outside as illustrated on FBD. This will cause the inner block to move towards axis of rotation.

We have N1  = 5 × 9.81 = 49.05 N

And  F = μ N1  = 0.2 × 49.05

                      = 9.810 N

By considering equilibrium ∑ Fx  = 0,      T + F = 5 × an

an  = r ω2 = 1.8 ω2

∴ T = 5 × 1.8 ω2 - 9.81

= 9 ω2 - 9.81          ----------- (1)

Let FBD of other block

F = 0.2 × 3 × 9.81 = 5.89 N

∑ Fx  = 0                   ∴ T = Fi  + F

= 3 × 1.2 ω2 + 5.89

= 3.6 ω2 + 5.89

∴ We have,    T = 9 ω2 - 9.81 = 3.6 ω2 + 5.89

                       9 ω2 - 3.6 ω2 = 5.89 + 9.81                     ----------- (2)

∴ ω2 =( 9.81 + 5.89 )/5.4 = 2.907

ω = 1.705 rad / sec

∴ N = (ω× 60) /2 π = 16.3 rpm

Substituting this value of ω in one of the equations for T, we obtain

 T = 9 ω2 - 9.81  = 16.35 N

Posted Date: 1/29/2013 2:43:31 AM | Location : United States

Related Discussions:- Determine the tension in the cord, Assignment Help, Ask Question on Determine the tension in the cord, Get Answer, Expert's Help, Determine the tension in the cord Discussions

Write discussion on Determine the tension in the cord
Your posts are moderated
Related Questions
Derive and solve a model of an insulated water tank with a changing level (i.e., changing tank volume). There is only one in ow stream with a flow rate of 1 kg/sec for t The

Q. Define Oxidation Process? Oxidation is defined as a loss of electrons, as when a metal goes from the metallic state to the corroded state. When a metal reacts with oxygen,

Q. How to observe water level? Site for installing gauges should be properly selected. The reach should be reasonably straight and of uniform cross· section and slope. The leng

Aggregate Production Planning: This unit provides the definition and physical significance of aggregate production planning. Further, this is illustrated that how the internal

Why is porter governor more sensitive than Watt Governor even the former has got an additional weight which will require more force to move sleeve than Watt governor?

Q. Use of High temperature material in Superheaters? Typically superheaters and reheaters provide service lives of approximately 15 years (i.e. half the expected service life o

how is varignons theorem useful in engineering mechanics

Q. Sustained Bending Moment? When sustained bending moments or axial thrust loadings are applied to the flanged joint during operation in sufficient magnitude to warrant consid