The two disks each have a mass of 23 k g and are attached at their centers by an

Question

The two disks each have a mass of 23kg  and are attached at their centers by an elastic cord that has a stiffness of k = 1.6kN/m . Determine the stretch of the cord when the system is in equilibrium and the angle ? of the cord. (Figure 1)

The two disks each have a mass of 23kg and are attached at their centers by an elastic cord that has a stiffness of k = 1.6. Determine the stretch of the cord when the system is in equilibrium and the angle ? of the cord. (Figure 1) Determine the stretch of the cord when the system is in equilibrium. Determine the angle?of the cord.

Explanation / Answer

At eq.

For object B:

kxsin(theta)=mg (along vertical direction)

So

xsin(theta)=0.140875

For object A:

90-theta-(90-tan^-1(4/3))=(53-theta)

So

kxsin(53-theta)=mgsin(37)=

So

xsin(53-theta)=0.084525

So

x(0.8cos(theta)-0.6sin(theta))=0.084525

So

0.8xcos(theta)-0.6*0.140875=0.084525

So

xcos(theta)=0.2113125

So

theta=tan^-1(0.140875/0.2113125)=33.69degrees

and

x=0.254 meters

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