Please answer fully! Thanks! 1. A box of mass 3.0 kg on a horizontal frictionles
ID: 1307467 • Letter: P
Question
Please answer fully! Thanks!
1. A box of mass 3.0 kg on a horizontal frictionless surface is attached to the end of a horizontal spring with a spring constant k = 8.0 kN/m. The other end of the spring is attached to a wall. The spring is initially stretched 15.0 cm to the right from its equilibrium position ( x = 0 m ) and released Determine (a) the frequency f of the oscillatory motion (b) its period T (c) the amplitude A (d) the maximum speed vmax of the motion (e) its maximum acceleration, amax (f) time taken by the mass to reach the equilibrium position for the first time.(g) acceleration at this specific time (h) The total mechanical energy associated with the oscillatory motion.
Explanation / Answer
mass m= 3 kg
k = 8000 N/m
aplitude A = 0.15 m
a)
frequency =( 1/2pi)*sqrt(k/m) = (1/6.28)*sqrt(8000/3) =8.22 Hz
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b)
peroid T = 1/f = 1/8.22 =0.1216 sec
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c)
amplitude A =0.15 m
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d)
maximum speed Vmax = A*sqrt(K/m) = 0.15*sqrt(8000/3) =7.745 m/s
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e)
maximum acceleration a = w^2*A = -(k/m)*A = -400 m/s^2
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f)
t = T/4 = 0.1216/4 =0.0304 sec
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g)
accecleration a = 0
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h)
total mechanical energy =0.5kA^2 =0.5*8000*0.15^2 = 90 J
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