Question

A hockey puck oscillates on a frictionless, horizontal track while attached to a horizontal spring. The puck has mass 0.160 kg and the spring has force constant 8.00 N/m. The maximum speed of the puck during its oscillation is 0.350 m/s. What is the amplitude of the oscillation? What is the total mechanical energy of the oscillation? What is the potential energy of the puck when the displacement of the glider is 0.0300 m? What is the kinetic energy of the puck when the displacement of the glider is 0.0300 m?

Answer 1

Explanation:

The given data is as follows.

     mass (m) = 0.160 kg,            spring constant (k) = 8 n/m,

     Maximum speed ($v_{m}$) = 0.350 m/s

Formula for angular frequency is as follows.

          $\omega = \sqrt{\frac{{k}{m}}$

    $\omega = \sqrt{\frac{{8}{0.160}}$

    $\omega$ = 7.07 rad/sec

(a) Formula to calculate the amplitude is as follows.

            $\nu_{max} = A \omega$

                  A = $\frac{\nu}{\omega}$

                      = $\frac{0.35}{7.07}$

                      = 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 = $\frac{1}{2}kA^{2}$

Putting the values into the above formula as follows.

            M.E = $\frac{1}{2}kA^{2}$

                   = $\frac{1}{2} \times 8 \times (0.05)^{2}$

                   = $9.8 \times 10^{-3}$ Joule

For x = 0.03,

As,     P.E = $\frac{1}{2} \times kx^{2}$

                = $\frac{1}{2} \times 8 \times (0.03)$

                = $3.6 \times 10^{-3}$

Hence, calculate the kinetic energy as follows.

            K.E = M.E - P.E

                  = ($9.8 \times 10^{-3}$ - $3.6 \times 10^{-3}$) J

                  = $6.2 \times 10^{-3}$ J

Thus, we can conclude that kinetic energy of the puck when the displacement of the glider is 0.0300 m is $6.2 \times 10^{-3}$ J.