Question

1) a) An object is at rest. Internal forces then cause it to separate into two moving pieces. If one piece has a linear momentum of +10 kg m/s, what is the linear momentum of the other piece? Explain your answer.

b) A frictionless, horizontal spring vibrates with simple harmonic motion; a frictionless, vertical spring does not, even if it obeys Hooke’s Law. Explain why. (BASE YOUR ANSWER ON THE DEFINITION OF SIMPLE HARMONIC MOTION).

c) When a crack forms in the ice covering a frozen pond, it typically gets bigger over time. This isn’t wave motion. Explain why. What would you observe if the crack did behave as a wave? (BASE YOUR ANSWERS ON THE DEFINITION OF A WAVE).

d) The first harmonic for standing waves on a certain string is 50 Hz. What would be the three lowest frequencies at which a wave source coupled to the string must vibrate in order to be in resonance with the string. Explain your answer.

* Please answer all parts.

Answer 1

a) The linear momentum of the other piece will be -10 kg m /s. To conserve the linear momentum, the total momentum must remain constant.(in the absence of external forces).

b) Simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

In the case of the vertical spring, apart from the restoring force, the gravitational force acts vertically downwards. This causes damping of the spring and the magnitude of the oscillation becomes zero in a short time. While for the horizontal spring, the gravitational force is perpendicular to the motion and does not contribute much as a damping force.

So, a frictionless, horizontal spring vibrates with simple harmonic motion; a frictionless, vertical spring does not, even if it obeys Hooke’s Law.

c) Wave is is a disturbance oscillate repeatedly in equal time interval about a stable equilibrium value/point. In the crack, there is no repetition. Or the position never comes back again; So, this is not a wave motion.

d) All the overtones are in the multiple of the first harmonic. So, the minimum values of frequency to get the resonance are

50, 100,150,200 (in Hz)

So, wave source can have these minimum values to get standing wave resonance.