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A 0.580 kg glider on an air track is attached to the end of an ideal spring with

ID: 1450279 • Letter: A

Question

A 0.580 kg glider on an air track is attached to the end of an ideal spring with force constant 455 N/m ; it undergoes simple harmonic motion with an amplitude of 4.40×102 m .

1-

Calculate the maximum speed of the glider.

Express your answer to three significant figures.

2-

Calculate the speed of the glider when it is at x = 1.30×102 m .

Express your answer to three significant figures.

3-

Calculate the magnitude of the maximum acceleration of the glider.

Express your answer to three significant figures.

4-

Calculate the acceleration of the glider at x = 1.30×102 m .

Express your answer to three significant figures.

5-

Calculate the total mechanical energy of the glider at any point in its motion.

Express your answer to three significant figures.

Explanation / Answer

1)     angular frequency , w = sqrt(k/m)

                                             =   sqrt(455/0.580)

                                            = 28   rad/sec

=>     maximum speed of the glider   = A * w

                                                      =   4.40 * 102 * 28

                                                    =   1.232   m/sec

2)    speed of the glider   = 28 * sqrt(0.0442 - 0.0132)

                                       =   1.177   m/sec

3)   magnitude of the maximum acceleration   = 0.044 * 28 * 28

                                                                      =   34.496   m/sec2

4)   acceleration of the glider   =   - 28 * 28 * 0.013

                                                   =   - 10.192    m/sec2

5)   total mechanical energy of the glider = 1/2 * 455 * 0.044 * 0.044

                                                                   =   0.4404   J