12.3 Stress, Strain, and Elastic Modulus

Find the compressive stress and strain at the base of Nelson’s column.

A 2.0-m-long wire stretches 1.0 mm when subjected to a load. What is the tensile strain in the wire?

If the normal force acting on each face of a cubical $1 .\text{0}-\text{m}^{3}$ piece of steel is changed by $1.0 \times 10^{7} \text{N} ,$ find the resulting change in the volume of the piece of steel.

Explain why the concepts of Young’s modulus and shear modulus do not apply to fluids.

Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in the table.

Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in the table.

A thin wire strung between two nails in the wall is used to support a large picture. Is the wire likely to snap if it is strung tightly or if it is strung so that it sags considerably?

Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in the table.

What type of stress are you applying when you press on the ends of a wooden rod? When you pull on its ends?

Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in the table.

Can Young’s modulus have a negative value? What about the bulk modulus?

The “lead” in pencils is a graphite composition with a Young’s modulus of approximately $1.0 \times 10^{9} \text{N} / \text{m}^{2} .$ Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.

By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping? (For nylon, $Y = 1.35 \times 10^{9} \text{Pa} .)$

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.20%. Calculate the force exerted by the juice per square centimeter if its bulk modulus is $1.8 \times 1 0^{9} \text{N} / \text{m}^{2} ,$ assuming the bottle does not break.

A vertebra is subjected to a shearing force of 500.0 N. Find the shear deformation, taking the vertebra to be a cylinder 3.00 cm high and 4.00 cm in diameter.

A 20.0-m-tall hollow aluminum flagpole is equivalent in strength to a solid cylinder 4.00 cm in diameter. A strong wind bends the pole as much as a horizontal 900.0-N force on the top would do. How far to the side does the top of the pole flex?

As an oil well is drilled, each new section of drill pipe supports its own weight and the weight of the pipe and the drill bit beneath it. Calculate the stretch in a new 6.00-m-long steel pipe that supports a 100-kg drill bit and a 3.00-km length of pipe with a linear mass density of 20.0 kg/m. Treat the pipe as a solid cylinder with a 5.00-cm diameter.

A 90-kg mountain climber hangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m long and its diameter is 1.0 cm, what is Young’s modulus for the nylon?

A copper wire is 1.0 m long and its diameter is 1.0 mm. If the wire hangs vertically, how much weight must be added to its free end in order to stretch it 3.0 mm?

The bulk modulus of a material is $1.0 \times 10^{11} \text{N}/\text{m}^{2} .$ What fractional change in volume does a piece of this material undergo when it is subjected to a bulk stress increase of $10^{7} \text{N}/\text{m}^{2} ?$ Assume that the force is applied uniformly over the surface.

During a walk on a rope, a tightrope walker creates a tension of $3.94 \times 1 0^{3} N$ in a wire that is stretched between two supporting poles that are 15.0 m apart. The wire has a diameter of 0.50 cm when it is not stretched. When the walker is on the wire in the middle between the poles the wire makes an angle of $5.0 °$ below the horizontal. How much does this tension stretch the steel wire when the walker is this posi…

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.0 cm. If the pressure on the surface is increased by 200 MPa, by how much does the radius of the sphere decrease?