A 220-g object attached to a spring oscillates on a frictionless horizontal tabl

Question

A 220-g object attached to a spring oscillates on a frictionless horizontal table with a frequency of 4.00 Hz and an amplitude of 21.0 cm.

1)

Calculate the maximum potential energy of the system.(Express your answer to three significant figures.)

JJ

2)

Calculate the displacement of the object when the potential energy is one-half of the maximum.(Express your answer to three significant figures.)

cmcm

3)

Calculate the potential energy when the displacement is 10.0 cm.(Express your answer to three significant figures.)

JJ

Explanation / Answer

A.

Max PE = 0.5*m*A^2*w^2

w = 2*pi*f = 2*pi*4 = 25.13

Max PE = 0.5*0.22*0.21^2*25.13^2 = 3.06 J

B.

Using energy conservation:

Ek = U

0.5*m*v^2 = 0.5*k*x^2

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

k = m*w^2

0.5*m*w^*(A^2 - x^2) = 0.5*k*x^2

2x^2 = A^2

x = A/sqrt 2

x = 0.21/sqrt 2 = 14.85 cm

C.

PE is given by:

PE = 0.5*k*x^2

PE = 0.5*m*w^2*x^2 = 0.5*0.22*25.13^2*0.1^2

PE = 0.69 J

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