A block of mass 1.4 kg is attached to a horizontal spring that has a force const

Question

A block of mass 1.4 kg is attached to a horizontal spring that has a force constant of 1.500 N/m as shown in the figure. The spring is compressed 2.6 cm and is then released from rest. Calculate the speed of the bock as it passes through the equilibrium position x = 0 if the surface is frictionless. Calculate the speed of the block as it passes through the equilibrium position if a constant friction force of 4.4 N retards its motion from me moment it is released. Calculate the speed of the bock as it passes through the equilibrium position x = 0 if me surface is frictionless. Calculate the speed of the bock as it passes through the equilibrium position if a constant friction force of 4.4 N retards its motion from the moment it is released.

Explanation / Answer

Ff = 18.1 N

from conservation of energy:

E(final) = Eintial - Ff x d + PE(spring)

E(final) = 0 - 18.1 x 0.026 + 1/2 x 1500 x 0.026^2 = 0.0364

E(final) = KE(block) = 0.0364

1/2 m v'^2 = 0.0364

v' = sqrt (2 x 0.0364/1.4) = 0.228 m/s

Hence, v' = 0.228 m/s

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