Septim
Dec3-10, 03:11 PM
1. Two springs each of natural length a and spring constant C are connected at one end(see figure).Consider a two dimensional displacement given by (x,y).
(a)Write the potential energy as a function of x and y.
(b)Find the force vector for a given (x,y) pair.
2. \vec{F}=-k\vec{x}(Hookes Law) \vec{x} is the displacement along the spring from equilibrium point. Magnitude wise l=L-L_{0}
3. First I assumed for the sake of simplicity potential energy as U(l)=(1/2)l^2C and summed them up since U is a scalar quantity. Then to find the force I differentiated U with respect to x and y respectively. But I am very curious if this solution is right cause a friend of mine has provided another solution which does not correspond with mine. I am including both of the solutions as attachments in jpeg format. By the way I need a vectorial solution for this thanks for your contribution in advance.
(a)Write the potential energy as a function of x and y.
(b)Find the force vector for a given (x,y) pair.
2. \vec{F}=-k\vec{x}(Hookes Law) \vec{x} is the displacement along the spring from equilibrium point. Magnitude wise l=L-L_{0}
3. First I assumed for the sake of simplicity potential energy as U(l)=(1/2)l^2C and summed them up since U is a scalar quantity. Then to find the force I differentiated U with respect to x and y respectively. But I am very curious if this solution is right cause a friend of mine has provided another solution which does not correspond with mine. I am including both of the solutions as attachments in jpeg format. By the way I need a vectorial solution for this thanks for your contribution in advance.