1.) A cube of lead (Pb) with dimensions 1 cm on an edge is dropped into a large

Question

1.) A cube of lead (Pb) with dimensions 1 cm on an edge is dropped into a large cubical container of mercury (Hg) which is of dimensions 1 m on an edge (a) After steady-state is reached, will it float or stay at the bottom of the conta (b) Determine the distance below the surface that the lead cube sinks into the Hg (c) If the cube is pressed down an infinitesimal distance further by a small externally applied force and then let go, show that the cube undergoes simple harmonic motion as a result of this action, and in the absence of any viscous damping determine the period and the frequency of this simple harmonic motion. (d) Imagine that this mechanically vibrating system, which produces acoustic waves in the fluid, is now attached to an electromagnetic resonator in order to produce resonance electromagnetic waves. In what region of the EM spectrum would these EM waves lie? (e) Sketch and explain the design of a detection system for these EM waves.

Explanation / Answer

The Restoring force developed in the two springs is

         F1 =-k1x

         F2 =-k2x

where x is the displacement

Total restoring force is

        F = F1 + F2 = - (k1+ k2)x

Therefore equivalent spring force constant of the system = k1 + k2

So that the angular frequency of the system is

               = ( (k1+k2)/ m )

f = /2pi

Time period, T = 1/f

T = 2(pi)* ( m/(k1+k2) )

Chegg policy, one question at a time

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.