Question

(a) Neglecting all resistive forces, determine the spring constant.
Answer should be in N/m.

(b) Neglecting all resistive forces, determine the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in figure(b).
Answer in m/s.

Answer 1

Please rate

a) h = 20.0 m
By conservation of energy,
(1/2) k x^2 = mgh
k = 2mgh/x^2
k = 2 * 0.024 * 9.8 * 20.0/0.140^2
k = 480 N/m (answer)

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b) h = 0.140 m
By conservation of energy,
(1/2) k x^2 = mgh + (1/2) m v^2
(1/2) 480 * 0.140^2 = 0.024 * 9.8 * 0.140 + (1/2) 0.024 * v^2
4.704 = 0.032928 + 0.012 v^2
0.012 v^2 = 4.671072
v = sqrt(4.671072/0.012)
v = 19.7 m/s (answer)