Question

An object with a mass m = 4.00 kg is attached to the end of a spring, and the spring is stretched an amount x; = 4.60 cm and then released. If the force constant for the spring is k = 520 N/m, determine the speed of the mass as it passes through the equilibrium position the first time for the following two cases. (a) The horizontal surface the object is sliding along is frictionless. m/s (b) The coefficient of kinetic friction between the horizontal surface and the object is uk = 0.250. m/s

Answer 1

mass (m) = 4 kg

xi = 4.6 cm

k = 520 N/m

a) let the sliding surface be frictionless

using work energy theorem

W_net = change in kinetic energy

(1/2)k(xi)^2 = (1/2)m(v)^2

520 * 0.046 * 0.046 = 4 v^2

v = 0.524 m/s

b) let the sliding surface be frictional , with coefficient of friction $\mu_k$ = 0.25

using work energy theorem

W_net = change in kinetic energy

(1/2)k(xi)^2 - $\mu_k$ m *g*xi= (1/2)m(v)^2

[520 * 0.046 * 0.046 ] - (0.25*4*9.8*0.046)= 4 v^2

0.64952 = 4v^2

V^2 = 0.16238

v = 0.403 m/s

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