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 = 1.60 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 = 6.60 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.60 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 = 3.30 cm?
m/s

Explanation / Answer

(a) PE = k x^2 / 2

= (860 N/m) (0.066 m)^2 / 2

= 1.87 J

(b) Applying energy conservation,
  
1.87 = 1.60 v^2 / 2

v = 1.53 m/s

(c) 1.87 = k x^2 /2 + m v^2 /2

1.87 = (860)(0.033^2)/2 + 1.60 v^2 / 2

v = 1.32 m/s

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