Respuesta :
Explanation:
The given data is as follows.
mass (m) = 0.160 kg, spring constant (k) = 8 n/m,
Maximum speed ([tex]v_{m}[/tex]) = 0.350 m/s
Formula for angular frequency is as follows.
[tex]\omega = \sqrt{\frac{{k}{m}}[/tex]
[tex]\omega = \sqrt{\frac{{8}{0.160}}[/tex]
[tex]\omega[/tex] = 7.07 rad/sec
(a) Formula to calculate the amplitude is as follows.
[tex]\nu_{max} = A \omega[/tex]
A = [tex]\frac{\nu}{\omega}[/tex]
= [tex]\frac{0.35}{7.07}[/tex]
= 0.05 m
Hence, value of amplitude is 0.05 m.
(b) Displacement = 0.030 m
Formula for mechanical energy is as follows.
M.E = [tex]\frac{1}{2}kA^{2}[/tex]
Putting the values into the above formula as follows.
M.E = [tex]\frac{1}{2}kA^{2}[/tex]
= [tex]\frac{1}{2} \times 8 \times (0.05)^{2}[/tex]
= [tex]9.8 \times 10^{-3}[/tex] Joule
For x = 0.03,
As, P.E = [tex]\frac{1}{2} \times kx^{2}[/tex]
= [tex]\frac{1}{2} \times 8 \times (0.03)[/tex]
= [tex]3.6 \times 10^{-3}[/tex]
Hence, calculate the kinetic energy as follows.
K.E = M.E - P.E
= ([tex]9.8 \times 10^{-3}[/tex] - [tex]3.6 \times 10^{-3}[/tex]) J
= [tex]6.2 \times 10^{-3}[/tex] J
Thus, we can conclude that kinetic energy of the puck when the displacement of the glider is 0.0300 m is [tex]6.2 \times 10^{-3}[/tex] J.
