Consider a spring of spring constant k. a) Find the potential energy storey in t
ID: 3162623 • Letter: C
Question
Consider a spring of spring constant k. a) Find the potential energy storey in the spring when it is stretched by a distance 2d from equilibrium. (b) Find the potential energy stored in the spring when it is compressed by a distance d/3 from equilibrium. A block of mass M is place on a frictionless table and two massless springs of length 2L each is attached to the block a shown in the figure. The spring constants of the two springs are k (for the one on the left) and 2k (for the one on the right). The figure is a top view of the setup. The free ends of the springs are attached to two vertical plates. The distance between the two plates is such that the strings are relaxed. Now the block is moved to the left by a distance L/2 as shown. Find the potential energy stored in the system at the new position. A massless spring of length L and spring constant k hangs from the ceiling. A block of mass M is attached to the free end of the spring and gently released. The spring stretExplanation / Answer
a] By energy conservation, E = 0.5mvo^2 + mgL sin theta
v = sqrt(2E/m)
= sqrt(vo^2 + 2gL sin theta)
b] again by energy conservation,
mgd sin alpha = 0.5 mv^2
d = [vo^2 + 2gL sin theta]/ (2g sin alpha)