Springs in Two Dimensions The ends of two identical springs are connected. Their

Question

Springs in Two Dimensions The ends of two identical springs are connected. Their unstretched lengths lare negligibly small and each has spring constant k. After being connected, both springs are stretched an amount L and their free ends are anchored at y 0 and z as shown (Figure 1) The point where the springs are connected to each other is now pulled to the position (ar, y). Assume that (z, y) lies in the first quadrant. Figure 1 of 1 Part A What is the potential energy of the two-spring system after the point of connection has been moved to position (a, y)? Keep in mind that the unstretched length of each spring l is much less than L and can be ignored (i.e., l L) Express the potential in terms of k, z, y, and L Submit Hints My Answers Give Up Review Part Incorrect, Try Again; 3 attempts remaining Part B Find the force F on the junction point, the point where the two springs are attached to each other. Express F as a vector in terms of the unit vectors i and j

Explanation / Answer

The potential energy will be the elastic potential energy which will be given as

U =0.5Kx2 ( Here x is the displacement from the mean position)

U = 0.5 K( L+x)2 + 0.5 K y2

Force could be calculated by using Hooks law

F = - K ( ( L+x) i + yj ))

  

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