A horizontal spring with force constant k = 630 N m is attached to a wall at one

Question

A horizontal spring with force constant k = 630 N m is attached to a wall at one end and to a block of mass m The block is released from rest from a position 3.70 cm beyond the spring's equilibrium position. 2.95 kg at the other end that rests on a norco tal surface. (a) If the surface is frictionless, what is the speed of the block as it passes through the equilibrium position? m/s (b) If the surface is rough and the coefficient of kinetic friction between the box and the surface is Ak-0.300, what is the speed of the block as it passes through the equilibrium position? m/s

Explanation / Answer

Given K = 630 N/m

mass m = 2.95 kg

displacement x = 3.7 cm = 0.037 m

a) from conservation of energy

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

1/2 * 630 * 0.037^2 = 1/2 * 2.95 * v^2

speed at equillibrium v = 0.5407 m/s

b) here mue = 0.3

frictional force fk = mue * m * g

fk = 0.3 * 2.95 * 9.8 = 8.673

from conservation of energy

1/2 * k * x^2 - (fk * x) = 1/2 * m * v^2

(1/2 * 630 * 0.037^2) - (8.673 * 0.037) = 1/2 * 2.95 * v^2

speed v = 0.2735 m/s

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