posted by .

A hanging wire made out of titanium with diameter 0.080 cm is initially 2.3 m long. When a 78 kg mass is hung from it, the wire stretches an amount 2.89 cm. A mole of titanium has a mass of 47.9 grams, and its density is 4.51 g/cm3. Based on these experimental measurements, what is the Young's modulus for titanium?

Find the effective spring stiffness of one interatomic bond in titanium.

  • Physics -

    Young's modulus = (tensile stress)/(strain)

    In this case the strain is
    (delta L)/L = 2.89cm/230 cm
    = 1.257*10^-2

    and the stress is

    sigma = (78*9.8 N)/[(pi/4)*(8^10^-4m)^2] = 764.4 N/5.027*10^-7 m^2)
    = 1.52*10^9 N/m^2

    So E = 1.21*10^11 N/m^2
    = 121 GPa

    A spring stiffness for an individual Ti-Ti interatomic pair can be estimated by dividing
    (Tensile force)/(area occupied by one molecule)
    by (stretch per intermolecular molecule pair).

    You will need a characteristic intermolecular distance or diameter for Ti atoms in the solid. Call it d. Get that from the number density of Ti atoms, n.
    d = n^(-1/3)

    n = [4.51 g/cm^3/(47.9g/mole)]*6.02*10^23 atom/mole = 5.56*10^22 atom/cm^3
    n^-1/3 = d = 2.6*10^-8 cm
    = 2.6*10^-10 m
    spring stiffness = k
    = E/d = 1.21*10^11/2.6*10^-10
    = 4.6*10^20 N/m

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?
  2. physics

    a metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 5.0 kg mass suspended from it. if the wire stretches 1.2 mm under the tension, what is the value of the young's modulus for metal?
  3. chemistry

    Titanium is used in airplane bodies because it is strong and light. It has a density of 4.55 g/cm^3. If a cylinder of titanium is 7.75 cm long and has a mass of 153.2 g, calculate the diameter of the cylinder. (V=pi*r^2*h, where V …
  4. Physics

    A 14.0 ohm resistor is made from a coil of copper wire whose total mass is 23.0 g. What is the diameter of the wire, and how long is it?
  5. physics

    A wire of diameter 0.65mm and length 6.0m stretches 10mm when 5.5kg is hung from it. What is the Young's modulus for the wire and what is the effective spring constant for the stretching wire
  6. Physics

    A horizontal wire is held taut by a mass M hanging from its end over a pulley. A harmonic wave of wavelength is produced on the wire by a 52 Hertz vibration. If the mass of the density of the wire is 8.0 x 10^-3 kg/m, what is M?
  7. Physics

    A steel (Young's modulus 2.0 x 1011 N/m2) wire is strung between two supports attached to a ceiling. Initially, there is no tension in the wire when it is horizontal. A 98-N picture is then hung from the center of the wire, as the …
  8. physics

    One mole of titanium (6 1023 atoms) has a mass of 48 grams, and its density is 4.54 grams per cubic centimeter, so the center-to-center distance between atoms is 2.60 10-10 m. You have a long thin bar of titanium, 2.4 m long, with …
  9. Physics

    1.A brass wire 80 cm long and 0.3 cm in diameter is used to hang an object weighing 6.5 x 10 ^5 dynes. Find stress, strain and young's modules. 2. To one end of a wire 1.2 m long and 0.4 cm in diameter is hung on object with a mass …
  10. Physics

    a wire 100 cm long and 0.2 cm in diameter is suspended from a support. a 10 kg mass is hung from the lower end of the wire. a find the stress b find the strain c young's modulus of elasticity

More Similar Questions