stress & strain

1) Here is a quote from an article on human
psychology. “*It’s a common belief that we need a certain amount of stress to
be able to function. This isn’t so, what we need is a certain amount of
pressure, and pressure is not stress. Stress is the result of too much
pressure.*” Please comment on this statement, from a physicist’s point of
view.

2) Draw a stress versus strain graph showing a very brittle material.

3) If you cut a spring in half, by how much would you change its spring constant (if at all)?

4) You might sometimes hear that liquids aren’t
compressible. Not so. The bulk modulus of water is 2.0 × 10^{9} N/m^{2}
and the bulk modulus for steel is 1.4 × 10^{11} N/m^{2}. Apply
a pressure of 1.95 × 10^{9} N/m^{2} to a cube of water and a
cube of steel, each identical in volume. By what percentage will each compress?

5) Imagine a large industrial machine that
operates with oil under high pressure. Find the strain experienced by the oil
when the pressure increases from 1.0 × 10^{5} Pa to 7.2 × 10^{5}
Pa. The bulk modulus for the oil is 1.0 × 10^{7} N/m^{2}.

6) The equation for shear stress has a F/A term, and the equation for bulk stress has a F/A term. However, while the bulk stress is considered a pressure, the shear stress is not. Why not?

7) In an effort to measure Young’s modulus, a 550
kg load is suspended from a wire of length 3.0 m and a cross section of 0.20 cm^{2}.
The wire stretches 0.40 cm. What is the wire’s modulus?

8) How much force can be supported by an
aluminum wire 0.10 cm in diameter without exceeding the proportional limit of 8.0
× 10^{7} N/m^{2}? Young’s modulus for aluminum is 7.0 × 10^{10}
N/m^{2}.

9) Is the shear modulus of steel greater or less than the shear modulus of Jell-O? How do you know?

10) A copper cube, 0.30 m on each side,
experiences a shear force of 6.0 × 10^{6} N/m^{2}. By what
distance will the block shear horizontally?