need help with part F through K, including number 2. Thanks! Att=0, a block of m
ID: 1796296 • Letter: N
Question
need help with part F through K, including number 2.
Thanks!
Att=0, a block of mass m =360 kg at rest on the end of a horizontal spring is pushed to the left compressing the spring a distance of 24.0 cm by a force of 105.6 N. The block is then released and the system undergoes SHM (simple harmonic motion). a) Determine the spring constant k I 57/ b) Determine the period and frequency of the motion. c) Determine the amplitude d) Determine the maximum velocity and the displacement x at which this occurs. 64 e l arr ido e) Determine the maximum acceleration and the displacement(s) x at which this occurs f Determine the total energy of the system. PE KE g) Determine the kinetic energy when x 0. 714 h) Determine the velocity of the block when x = 0. i) Determine the potential energy when x 14 cm. j) Determine the kinetic energy when x 14 cm. k) Determine the velocity of the block when x = 14 cm. 2. A simple pendulum has a length of 0.450 m. What is its period and frequency?Explanation / Answer
1)
m=3.6 kg
force, F=105.6 N
compression, x=24cm
a)
F=k*x_max
105.6=k*0.24
===> k=440 N/m
b)
time period, T=2pi*sqrt(m/k)
T=2pi*sqrt(3.6/440)
T=0.57 sec
frequency, f=1/T
f=1/(0.57)
f=1.76 Hz
c)
ampitude, A=24cm
d)
Vmax=A*w
=0.24*(2pi/T)
=0.24*(2pi/0.57)
=2.64 m/sec
at x=0 ==> velocity is maximum
e)
amax=w^2*A
=(2pi/T)^2*A
=(2pi/0.57)^2*(0.24)
=29.2 m/sec^2
at x=A(maximum displacement) ==> acceleration is maximum
f)
T.E=1/2*K*A^2
=1/2*440*0.24^2
=12.67 J
g)
at x=0, T.E=K.E=1/2*m*v_max^2
K.E=12.67 J
h)
at x=0, velocity is maximam,
vmax=2.64 m/sec
i)
at x=14cm
P.E= 1/2*m*w^2*x^2
=1/2*3.6*(2pi/0.57)^2*0.14^2
=4.29 J
j)
here,
T.E=K.E+P.E
12.67=K.E+4.29
==> K.E=8.38 J
k)
at x=14cm
velocity v=w*sqrt(A^2-x^2)
v=(2pi/0.57)*sqrt(0.24^2-0.14^2)
v=2.15 m/sec
2)
period T=2pi*sqrt(l/g)
T=2pi*sqrt(0.45/9.8)
T=1.34 sec
and
frequency f=1/T
f=1/(1.34)
f=0.743 Hz
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