The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a total distance of 15.6 cm, what is its maximum speed when the engine is running at 3 480 rpm?
a. 28.4 m/s
b. 14.2 m/s
c. 56.9 m/s
d. 7.11 m/s
e. 3.55 m/s
[Ques. 2] An electron is moving at a speed of 4.8 106 m/s at an angle of 30.0 with respect to a uniform magnetic field of 9.2 104 T. What is the radius of the resulting helical path? (me = 9.11 1031 kg, qe = 1.60 1019 C)
a. 2.6 cm
b. 3.8 cm
c. 5.5 cm
d. 1.5 cm
e. 2.9 cm
[Ques. 3] An object moving in simple harmonic motion has an amplitude of 0.0450 m and a maximum acceleration of 40.0 m/s2 . What is the frequency of the system?
a. 14.9 Hz
b. 187 Hz
c. 4.75 Hz
d. 11.9 Hz
e. 1.80 Hz
[Ques. 4] A proton with initial kinetic energy KE is moving in circular motion in a uniform magnetic field. When it has completed one eighth of a revolution, what is its kinetic energy?
a. 1.4KE
b. 0.71KE
c. KE
d. The value is not given.
[Ques. 5] A mass on a spring vibrates in simple harmonic motion at a frequency of 3.2 Hz and an amplitude of 6.4 cm. If a timer is started when its displacement is a maximum (hence x = 6.4 cm when t = 0), what is the displacement of the mass when t = 3.3 s?
a. zero
b. 5.95 cm
c. 2.36 cm
d. 2.53 cm
[Ques. 6] At the Fermilab accelerator in Weston, Illinois, singly-charged ions with momentum 3.3 1016 kgm/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What B field must be used to maintain the ions in this orbit? (qion = 1.60 1019 C)
a. 5.3 T
b. 2.1 T
c. 2.1 T
d. 0.19 T
e. 0.48 T
[Ques. 7] A mass on a spring vibrates in simple harmonic motion at a frequency of 4.26 Hz and an amplitude of 3.00 cm. If a timer is started when its displacement is a maximum (hence x = 3.00 cm when t = 0), what is the acceleration magnitude when t = 3.74 s?
a. zero
b. 0.732 m/s2
c. 39.2 m/s2
d. 19.6 m/s2
e. 10.5 m/s2
[Ques. 8] A proton, mass 1.67 1027 kg and charge +1.6 1019 C, moves in a circular orbit perpendicular to a uniform magnetic field of 0.86 T. Find the time for the proton to make one complete circular orbit.
a. 2.4 108 s
b. 7.6 108 s
c. 3.8 108 s
d. 1.2 108 s
e. Not enough information is given.
[Ques. 9] A mass on a spring vibrates in simple harmonic motion at a frequency of 8.0 Hz and an amplitude of 2.0 cm. If a timer is started when its displacement is a maximum (hence x = 2.0 cm when t = 0), what is the speed of the mass when t = 3.0 s?
a. zero
b. 100 m/s
c. 3.0 m/s
d. 2.0 m/s
e. 50 m/s
[Ques. 10] In a mass spectrometer, an ion will have a smaller radius for its circular path if
a. its speed is greater.
b. its mass is greater.
c. its charge is greater.
d. the magnetic field is weaker.
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