Map University Physics Kesten Tauck presented by Sapling Learning A 225-g object

Question

Map University Physics Kesten Tauck presented by Sapling Learning A 225-g object is attached to a spring that has a force constant of 77.5 N/m. The object is pulled 7.75 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed of the object. Number m/s Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibriunm position as zero, positions to the right as positive, and positions to the left as negative. Number Number cm cm Previous Give Up & View Solution O Check Answer Next Exit Hint

Explanation / Answer

given

m = 225 g = 0.225 kg
K = 77.5 N/m
A = 7.75 cm = 0.0775 m

a) use conservation of energy

(1/2)*m*v_max^2 = (1/2)*k*A^2

v_max = A*sqrt(k/m)

= 0.0775*sqrt(77.5/0.225)

= 1.44 m/s

b)

again use conservation of energy

(1/2)*m*v^2 + (1/2)*k*x^2 = (1/2)*k*A^2

(1/2)*m*(v_max/3)2 + (1/2)*k*x^2 = (1/2)*k*A^2

(1/2)*0.225*(1.44/3)^2 + (1/2)*77.5*x^2 = (1/2)*77.5*0.0775^2

x = 0.0731 cm or -0.0731 cm

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