A horizontal spring attached to a wall has a force constant of k = 760 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 760 N/m. A block of mass m = 1.30 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 = 6.20 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.20 cm from equilibrium.
J

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

(c) What is the speed of the block when it is at a position xi/2 = 3.10 cm?
m/s

Explanation / Answer

(a) potential energy of the spring is E=kx^2/2=760*0.062^2/2=1.46 J
(b) when block passes thorough the equilibrium, spring has zero potential energy, which was transferred to the kinetic energy of the block

E=mv^2/2=1.71 J --> v^2=2*1.46/1.3=2.24 --> v=sqrt(2)=1.5 m/s

(c)
Total energy = potential + kinetic=1.46

--> kx^2/2+mv^2/2=1.46, when x=0.031m
--> mv^2=2*1.46-760*0.031^2=2.189
--> v^2=2.189/1.3=1.68
--> v=sqrt(1.68)=1.3 m/s

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