You attach one end of a spring with a force constant k = 813 N/m to a wall and t

Question

You attach one end of a spring with a force constant

k = 813 N/m

to a wall and the other end to a mass

m = 2.52 kg

and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position

xi = 6.76 cm

from equilibrium and release it.

(a) Determine the potential energy stored in the spring before the block is released.
J

(b) Determine the speed of the block as it passes through the equilibrium position.
m/s

(c) Determine the speed of the block when it is at a position

xi/4.

m/s

Explanation / Answer

a)

when the spring is stretched elastic potential energy is stored in spring

Ui = 0.5*k*i^2 = 0.5*813*0.0676*0.0676 = 1.85760744 J = 1.86 J

part b)

at eqilibrium position = 0

PEf = Uf = 0

from work energy theorem change in PE = Work done = 0.5*m*v^2

0.5*m*v^2 = 1.86

0.5*2.52*v^2 = 1.86

v = 1.214 m/s   <-------answer

c) at x = xi/4 = 6.96/4 = 1.74 cm = 0.0174 m

Uf = 0.5*k*x^2 = 0.5*813*0.0174*0.0174 = 0.12307194 J

W = Ui - Uf

0.5*m*v^2 = 1.76 - 0.123

0.5*2.52*v^2 = 1.637

v = 1.14 m/s <----answer

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