A horizontal spring attached to a wall has a force constant of k = 860 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 860 N/m. A block of mass m = 1.20 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 = 5.80 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 5.80 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 = 2.90 cm?
_____m/s ?

Explanation / Answer

a)

stored potential energy = (1/2)kx^2

PE = (1/2)*860*(0.058)^2 = 1.446 J

b)

let speed of block = v

so (1/2)kx^2 = (1/2)mv^2

v = x*sqrt(k/m) = 0.058*sqrt(860/1.2)

v = 1.55 m/s

c)

let speed of block = v

so (1/2)kx^2 = (1/2)mv^2

v = x*sqrt(k/m) = 0.029*sqrt(860/1.2)

v = 0.776 m/s

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