A 5.00-kg object is attached to one end of a horizontal spring that has a neglig

Question

A 5.00-kg object is attached to one end of a horizontal spring that has a negligible mass and a spring constant of 390 N/m. The other end of the spring is fixed to a wall. The spring is compressed by 10.0 cm from its equilibrium position and released from rest.

1) What is the speed of the object when it is 8.00 cm from equilibrium? (Express your answer to three significant figures.)

2) What is the speed when the object is 5.00 cm from equilibrium? (Express your answer to three significant figures.)

3) What is the speed when the object is at the equilibrium position? (Express your answer to three significant figures.)

Explanation / Answer

1)

xi = initial compression = 10 cm = 0.1 m

xf = final compression = 8 cm = 0.08 m

k = spring constant = 390 N/m

m = mass = 5 kg

v = speed gained = ?

using the conservation of energy

initial spring energy = final spring energy + kinetic energy of object

(0.5) k xi2 = (0.5) k xf2 + (0.5) m v2

(390) (0.1)2 = (390) (0.08)2 + (5) v2

v = 0.529 m/s

2)

xi = initial compression = 10 cm = 0.1 m

xf = final compression = 5 cm = 0.05 m

k = spring constant = 390 N/m

m = mass = 5 kg

v = speed gained = ?

using the conservation of energy

initial spring energy = final spring energy + kinetic energy of object

(0.5) k xi2 = (0.5) k xf2 + (0.5) m v2

(390) (0.1)2 = (390) (0.05)2 + (5) v2

v = 0.765 m/s

3)

xi = initial compression = 10 cm = 0.1 m

xf = final compression = 0 m

k = spring constant = 390 N/m

m = mass = 5 kg

v = speed gained = ?

using the conservation of energy

initial spring energy = final spring energy + kinetic energy of object

(0.5) k xi2 = (0.5) k xf2 + (0.5) m v2

(390) (0.1)2 = (390) (0)2 + (5) v2

v = 0.883 m/s

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