A 0.250-kg block resting on a frictionless, horizontal surface is attached to a

Question

A 0.250-kg block resting on a frictionless, horizontal surface is attached to a spring whose force constant is 83.8 N/m as in the figure below. A horizontal force Frightarrow causes the spring to stretch a distance of 5.46 cm from its equilibrium position. Find the magnitude of Frightarrow. What is the total energy stored in the system when the spring is stretched? Find the magnitude of the acceleration of the acceleration of the block immediately after the applied force is removed. Find the speed of the block when it first reaches the equilibrium position.

Explanation / Answer

a)

F = kx = 83.8N/m x 0.0546m = 4.57548 N

b)

U = 1/2kx^2 = 0.12491 J

c)

a = F/m = 4.57548N / 0.250kg = 18.30m/s^2

d)

KE = 1/2mv^2
0.12491 J = 1/2*0.250 kg*v^2

v^2 = 0.99928

v = 0.9996 m/s

v = 99.96 cm/sec

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