Physics <span title="Problems..Density,Elasticity..Help">Problems..Density,Elastic...</span> Please.?

Question

1) A steel bar is placed vertically in the basement of a building to keep the floor above from sagging. The load on the beam is 5.8x10^4 N, the length of the beam is 2.5 m, and the cross-sectional area of the beam is 7.5x10^-3 m^2. Find the vertical compression of the beam.

2) A nylon tennis string on a racket is under a tension of 250N. If its diameter is 1mm, how much is it lengthened from its untensioned length of 30 cm?

3) A sphere of copper is subjected to 100MPa. The copper has a bulk modulus of 170 GPa. By what fraction of the volume of the sphere change?

4) Atmospheric pressure on Venus is about 90 times that on Earth. A steel sphere with a bulk modulus of 160 GPa has a volume of 1 cm^3 on Earth. If it were put in a pressure chamber and the pressure increased to that of Venus (9.12 MPa), how much is its volume change?

5) At depths of 2000m in the sea, the pressure is about 200 times atmospheric pressure (1x10^5). By what percentage does an iron bathysphere's volume change at this depth?

6) A 1200-kg concrete slab that measures 2m x 1m x .2m is delivered to a building construction. Does it contain steel reinforcing rod or is it plain concrete? If not pure concrete, how much steel is present? Express your answer in terms of percentage.

Thank you very much to those who'll be helping me.. ^_^

Pls. explain the steps u did to find the final answer...

Answer 1

EDIT:  Corrected the value of cross-sectional area to 7.5*10^-3 m²

1) The stress is 5.8*10⁴ N / 7.5*10^-3 m²  The strain is S/E where E is Young&#039;s modulus, which for steel is about 200*10⁹ N/m², the compression is length times strain, so the result is 5.8*10⁴ * 2.5 / 7.5*10^-3 * 200*10⁹ m

2) For nylon E is  about 5*10⁹ N/m².  Stress is again tension divided by area, and strain is stress/E.  Extension = length times strain.

3)  The fractional change of volume is pressure divided by bulk modulus.

4) The fractional volume change is pressure divided  by bulk modulus.  The actual volume change is the fractional change time the initial volume (1 cm³)

5) The bulk modulus of iron is 1.6*10⁹ N/m².  The fractional change is pressure (10⁵ N/m²) divided by the bulk modulus.  The percent change is 100 times the fractional change

6)  The volume of the slab is 0.4 m³.    The density of concrete is approx 2400 kg/m³.  If the slab were all concrete, it would have a mass of 960 kg, therefore it must contain steel.  If you assume the volume of steel is much less than the volume of concrete, then the difference of 240 kg is steel.  At a density of 8,000 kg/m³ that means the volume of steel is 0.03 m³, less than a tenth the volume of concrete, so the approximation is valid.

EDIT:  If you need a more accurate approach, note that the mass of the slap is M(slab) =  ÃƒÂÃ‚(concrete)*V(concrete) + ρ(steel)*V(steel).  But V(concrete) + V(steel) = V(slab).  Then V(concrete) = V(slab) - V(steel), so

M(slab) =  ÃƒÂÃ‚(concrete)*[V(slab) - V(steel)] + ρ(steel)*V(steel)

M(slab) =  ÃƒÂÃ‚(concrete)*V(slab) - ρ(concrete)*V(steel) + ρ(steel)*V(steel)

M(slab) =  ÃƒÂÃ‚(concrete)*V(slab) + V(steel)*[ρ(steel) - ρ(concrete)]

V(steel) = [M(slab) - ρ(concrete)*V(slab)] / [ρ(steel) - ρ(concrete)]

V(steel) = 240 / (8000 - 2400) = 0.0429 m³ and M(steel) = 0.0429*8000 = 343 kg

Answer 2

yuy.. tlgang nilagay lhat... physics assignment! i thought i was the only one doing this... r u from quantum? cnu toh? honestly?! :) IX! &lt;3 ! :)

* check number one. it should be 7.5*10^-3 ... note: NEGATIVE 3 is the exponent.