1. (10 points) A particle of mass m is attached between two identical, ideal springs of relaxed length L and constant k

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1 10 Points A Particle Of Mass M Is Attached Between Two Identical Ideal Springs Of Relaxed Length L And Constant K 1 (56.16 KiB) Viewed 21 times

1. (10 points) A particle of mass m is attached between two identical, ideal springs of relaxed length L and constant k The particle and springs lie on a frictionless horizontal surface. The particle is at equilibrium at the origin between the two relaxed springs (a) (1 point) Use the figure and your knowledge of spring forces to describe the motion of the particle if displaced from equilibrium at the origin by a distance x along the x-axis. 6) (1 point) Draw the FBD for the particle on the xy-plane. The particle is supported by the table, so you can ignore its weight and the normal force, both of which are perpendicular to the table (c) (3 points) The potential energy of the 2-spring (conservative) system is: U(x) = kx2 + 2kL(L-Vx2 + 2?). Based on the potential energy, show that, when displaced from equilibrium along the x - axis, the force on the particle is in the negative x-direction and has magnitude: F(x) = -2kx (1 - 1x2 + L Overhead view (d) (2 points) Let L = 1.50 m, k = 45.0 N/m, m= 1.35 kg The particle is displaced by x = 0.750 m to the right of the origin, and then released from rest. Show that its speed as it reaches x = 0, is v = 1.45 x=0 (e) (3 points) Show how to obtain the functional form of the force F(x) from the geometry and your knowledge of spring forces. Recall each spring exerts a force F=-kld-L) when stretched a distance d from its relaxed length L (Hint: Think of the net force on the x and y-directions) =