05.3 Consider a 2.0 kg mass on a spring on a horizontal surface. The spring has
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Question
05.3 Consider a 2.0 kg mass on a spring on a horizontal surface. The spring has spring constant 36 N/m. The static coefficient of friction between the mass and the surface is µS = 0.30 and the kinetic coefficient of friction is µK = 0.20.
(a) What is the largest extension x0 of the spring such that the mass is held in place by friction?
(b) If the mass is at x0 = 10 cm and given a short push so that its initial velocity is 1.2 m/s to the left, use energy considerations to determine where the mass first comes to a stop.
Explanation / Answer
a)
spring force = static frictional force
k Xo = µS Fn
k Xo = µS mg since Fn = mg
36 Xo = (0.3) (2) (9.8)
Xo = 0.163 m
b)
Vo = initial velocity = 1.2 m/s
Xo = initioal extension = 10 cm = 0.10 m
W = work done by friction = fk d
Using conservation of energy
initial KE + initial spring energy = work done by friction + final spring energy
(0.5) m Vo2 + (0.5) k Xo2 = µK mg d + (0.5) k d2
(0.5) (2) (1.2)2 + (0.5) (36) (0.10)2 = (0.20) (2) (9.8) d + (0.5) (36) d2
d = 0.21 m
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