4) When a 5 kg mass is hung on a spring, it stretches by 4.0 cm a) What is the s

Question

4) When a 5 kg mass is hung on a spring, it stretches by 4.0 cm a) What is the spring constant of the spring? (5 Points) c) How fast is the mass moving as it passes back through the equilibri d) How much p oscillating up and down by stretching it an additional 4.0 c m and releasing it, what is the period of oscillation? (5 Points) point? (5 Points) otential energy is in the assembly when it is at its extreme displacement? (5 Points) If you want to make the system tear itself apart, what is the highest frequeney (f not o) that can be used as a driving force to cause the system to resonate? (5 Points) o e)

Explanation / Answer

4. (a) Fnet = k x - m g = 0

k (0.04) = (5)(9.8)

k = 1225 N/m

(b) T = 2 pi sqrt( m /k ) = 0.40 sec  

(C) w = 2 pi / T = 15.65 rad/s

v_max = w A = 15.65 x 0.04 =0.63 m/s

(d) Spring potential energy = k x^2 / 2 = 1225 (0.08^2)/ 2

= 3.92 J  

Gravitational PE (considering equilibrium as reference point)

= - 5 x 9.8 x 0.04 = - 1.96 J

total PE = 1.96 J

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