A 0.36-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m.The block is initially displaced 6 cm from the equilibrium point and then released to set up a simple harmonic motion.A frictional force of 0.3 N exists between the block and surface.What is the speed of the block when it passes through the equilibrium point after being released from the 6-cm displacement point?

A) 0.55 m/s
B) 0.39 m/s
C) 0.77 m/s
D) 0.3 m/s
E) 2.19 m/s

Question

A 0.36-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m.The block is initially displaced 6 cm from the equilibrium point and then released to set up a simple harmonic motion.A frictional force of 0.3 N exists between the block and surface.What is the speed of the block when it passes through the equilibrium point after being released from the 6-cm displacement point?
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A) 0.55 m/s
B) 0.39 m/s
C) 0.77 m/s
D) 0.3 m/s
E) 2.19 m/s

Quizplus · Accepted Answer

Explanation:The mechanical energy of the block is conserved, so:$$1/2kA^2=1/2mv^2+f_kd$$$$v=\sqrt{\frac{kA^2-2f_kd}{m}}=\sqrt{\frac{(40	ext{ N/m})(0.06	ext{ m})^2-2(0.3	ext{ N})(0.06	ext{ m})}{0.36	ext{ kg}}}=0.55	ext{ m/s}$$

A 036-Kg Block Rests on a Frictionless Level Surface and Is