A block of mass m = 0.810 kg is fastened to an unstrained horizontal spring whos
ID: 1559554 • Letter: A
Question
A block of mass m = 0.810 kg is fastened to an unstrained horizontal spring whose spring constant is k = 80.0 N/m. The block is given a displacement of +0.120 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.
(a) What is the force (magnitude and direction) that the spring exerts on the block just before the block is released?
N
(b) Find the angular frequency of the resulting oscillatory motion.
rad/s
(c) What is the maximum speed of the block?
m/s
(d) Determine the magnitude of the maximum acceleration of the block.
m/s2
Explanation / Answer
given
m = 0.81 kg
k = 80 N/m
Amplitude, A = 0.12 m
a) using Hook's law
F = -k*x
= -80*0.12
= -9.6 N
b) w = sqrt(k/m)
= sqrt(80/0.81)
= 9.94 rad/s
c) Vmax = A*w
= 0.12*9.94
= 1.19 m/s
d) a_max = A*w^2
= 0.12*9.94^2
= 11.8 m/s^2
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