A horizontal spring attached to a wall has a force constant of k = 880 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 880 N/m. A block of mass m = 1.90 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 = 6.40 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.40 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 = 3.20 cm?
m/s

Explanation / Answer

A) PE = 0.5*k*A^2

k is the spring constant = 880 N/m

A is the amplitude = 0.064 m

PE = 0.5*880*0.064^2 = 1.80224 J

B) KEmax = PEmax = 1.80224 J

0.5*m*v^2 = 1.80224

v = sqrt(1.80224/(0.5*1.9)) = 1.37 m/s

C) v = w*sqrt(A^2-x^2)

x = 0.032 m   and A = 0.064 m

w =sqrt(k/m) = sqrt(880/1.9) = 21.52 rad/s

v = 21.52*sqrt(0.064^2-0.032^2) = 1.192 m/s

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