Here\'s the question An object is attached to four springs. One end of each spri
ID: 2262621 • Letter: H
Question
Here's the question
An object is attached to four springs. One end of each spring is attached to the object, while the other is anchored to a point in the x-y plane. The natural lengths of all springs are zero, i.e. the magnitude of the force generated by the ith spring is given by: where |i is the length of the ith spring. The anchor points and spring constants of the four springs are: Spring constants and anchoring points What are the coordinates (x,y) of the system's equilibrium point? [in meters] The system is in equilibrium if the mass is located at( , )Explanation / Answer
Let object's point be (x,y)
let i be unit vector along x direction and j be unit vector along y direction
F1=k1*[ (x-2)i + (y-3)j]
F2=k2*[(x-1)i + (y-1)j]
F3=k3*[(x)i +(y+3)j]
F4=k4*[(x-5)i + (y-5)j]
For equilibrium sum of all forces is equal to zero
Thus,
F1+F2+F3+F4=0
1.2(x-2)+1.5(x-1)+3.1(x)+0.5(x-5)=0
6.3x-6.4=0
x=1.02
1.2(y-3)+1.5(y-1)+3.1(y+3)+0.5(y-5)=0
6.3y+1.7=0
y=-0.27
Therefore point of quilibrium =(1.02,-0.27)