A spring hangs freely with a hook at its end at rest at position, y= 0.0. A 1 kg

Question

A spring hangs freely with a hook at its end at rest at position, y= 0.0. A 1 kg mass is then attached to the hook on the spring and the hook is now at y = -0.4 m. The system is at rest.

a. Calculate the spring constant.

b. Calculate the mechanical energy stored in the spring.

An external force lowers the mass to position y= -0.5 m and the mass is then released.

c. Calculate the mechanical energy stored in the spring at the moment the mass is released.

d. Calculate the speed of the mass as it passes through the point y = -0.4 m.

e. Calculate the maximum height reached by the mass.

f. Calculate the acceleration of the mass at the moment it reaches its maximum height.

Explanation / Answer

(A) F_net = k x - m g = 0

k (0.4) = (1)(9.8)

k = 24.5 N/m

(B) U = k x^2 / 2 = (24.5)(0.4^2)/2

U = 1.96 J

(C) U = (24.5)(0.5^2)/2

U = 3.0625 J

(D) A = 0.1 m , w = sqrt(k/m) = 4.95 m/s

v_max = A w = 0.495 m/s

(e) H_max = 0.3 m

(f) a = (24.5)(0.1)/1 = 2.45 m/s^2 downwrad

or a = - 2.45 m/s^2

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