A block of mass m = 2.00 kg is attached to a spring of force constant k = 445 N/

Question

A block of mass m = 2.00 kg is attached to a spring of force constant k = 445 N/m as shown in the figure below. The block is pulled to a position xi = 5.90 cm to the right of equilibrium and released from rest.

(a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless.

A block of mass m = 2.00 kg is attached to a spring of force constant k = 445 N/m as shown in the figure below. The block is pulled to a position xi = 5.90 cm to the right of equilibrium and released from rest. (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless.

Explanation / Answer

in the first case, we can use conservation of energy; the PE when the spring is extended equals the KE when the block passes through equilibrium

1/2 k x ^2 = 1/2 m v^2

v = Sqrt[ k x^2/m] = Sqrt[445N/m x 0.059m^2 / 2kg] = 0.88 m/s

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