A horizontal spring attached to a wall has a force constant of k = 840 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 840 N/m. A block of mass m = 2.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below.

(a) The block is pulled to a position xi = 5.20 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 5.20 cm from equilibrium.

in J.

(b) Find the speed of the block as it passes through the equilibrium position.

in m/s.

(c) What is the speed of the block when it is at a position xi/2 = 2.60 cm?

in m/s.

Explanation / Answer

(a) potential energy of the spring is E=kx2/2=840*0.0522/2=1.13 J
(b) when block passes thorough the equilibrium, spring has zero potential energy, which was transferred to the kinetic energy of the block

E=mv2/2=1.13 J

v2= 2*1.13/2 = 1.13

v=sqrt(1.13)=1.063 m/s

(c)
Total energy = potential + kinetic=1.13

kx2/2+mv2/2=1.13, when x=0.031m
mv2=2*1.13-840*0.0262=1.69
v2=1.69/2=0.84
v=sqrt(0.84)=0.91 m/s

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