One mole of titanium (6 multiply 1023 atoms) has a mass of 48 grams, and its den

Question

One mole of titanium (6 multiply 1023 atoms) has a mass of 48 grams, and its density is 4.54 grams per cubic centimeter. You have a long thin bar of titanium, 2.3 m long, with a square cross section, 0.07 cm on a side. You hang the rod vertically and attach a 30 kg mass to the bottom, and you observe that the bar becomes 1.15 cm longer. Calculate the effective stiffness of the interatomic bond, modeled as a "spring": ks = Next you remove the 30 kg mass, place the rod horizontally, and strike one end with a hammer. How much time will elapse before a microphone at the other end of the bar will detect a disturbance? t =

Explanation / Answer

a)

Y = F*L / delta L*A

= 30*9.8*2.3 / 0.0115*(0.07*10^-2)^2

= 1.2*10^11 N/m^2

d^3 = M / N*rho

=48 / 6*10^23*4.54

=1.762*10^-23

d = 2.602*10^-10 m

Ks = Y*d

=1.2*10^11*2.602*10^-10

=31.224 N/m

======================================================

b)

m = M / N

= 0.048 / 6*10^23

= 8*10^-26 kg

v = d*sqrt(Ks /m)

=2.602*10^-10*sqrt(31.224/8*10^-26)

= 5140.514m/s

delta T = delta x / v

= 2.3 / 5140.514

= 4.474*10^-4 s

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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