# Worksheet: Stress, Strain, and Elastic Modulus

In this worksheet, we will practice calculating the change in the length and the volume of a material given properties such as its Young's modulus and bulk modulus.

**Q3: **

Two rods, one made of brass and the other of lead, have the same dimensions. When a particular stress is applied to the brass rod, it stretches by 0.18 mm. How much does the lead rod stretch under the same stress? Use a value of Pa for the Young’s modulus of brass and use a value of Pa for the Young’s modulus of lead.

**Q4: **

Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod
is 2.0 m long and has cross-sectional area of 9.1 mm^{2}. A tensile force of 10 kN is applied at
each end of the combination. Use a value of Pa for the Young’s modulus of steel and
a use a value of Pa for the Young’s modulus of aluminum to determine the effects of
the force on the rods.

Find the stress in the rods.

- A
N/m
^{2} - B
N/m
^{2} - C
N/m
^{2} - D
N/m
^{2} - E
N/m
^{2}

Find the strain in the rods.

- A
- B
- C
- D
- E

Find the elongation of the steel rod.

Find the elongation of the aluminum rod.

**Q5: **

During a walk on a rope, a tightrope walker creates a tension of N in a steel wire that is stretched between two supporting poles that are 15.0 m apart. The wire has a diameter of 0.500 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 below the horizontal. Under tension, steel has a Young’s modulus of Pa. How much does the tension in the wire stretch the wire when the walker is this position?

**Q7: **

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 mass drill bit and a m 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. The Young's Modulus of Steel is Pa.

**Q10: **

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 equivalently to a horizontal 900.0-N force acting on the the top of the pole. How far to the side does the top of the pole flex? Use a value of Pa for the shear modulus of aluminum.

**Q11: **

A steel suspension rod of a suspension bridge is 23 m long. The suspension rod must not stretch by more than 1.1 cm when a truck with a mass of kg passes over the section of the bridge suspended from the rod. What diameter must the rod have if it supports the entire weight of such a truck? Use a value of Pa for the Young’s modulus of steel.

**Q12: **

A physicist with a mass of 78.0 kg places himself and kg of equipment at the top of a 640 m high TV broadcast antenna to perform experiments on gravity. If the antenna is modeled as a steel cylinder of radius 0.1700 m, by how much is it compressed due to the weight of the physicist and his equipment? Use a value of Pa for the Young’s modulus of steel.

**Q19: **

A boy with a mass of 35 kg falls vertically downward
through 3.7 m.
The boy lands on one foot and comes
to rest in 0.12 s after he hits the ground,
decelerating uniformly. The total cross-sectional area of the bones in the boy’s
legs just above his ankles is 3.4 cm^{2}.
What is the compressive stress in these bones?

- A Pa
- B Pa
- C Pa
- D Pa
- E Pa

**Q24: **

A sculpture that has a weight of
10.0 kN
rests on the level top of a 6.00 m
high vertical column that has
a cross-sectional area of
0.200 m^{2}.
The column has a density of
kg/m^{3}.

What is the compressive stress applied to a cross-sectional layer of the column 3.0 m below the base of the sculpture?

Find the compressive strain of the column section extending from the base of the sculpture to 3.0 m vertically below that point. Use a value of kPa for the Young’s modulus of granite.

- A
- B
- C
- D
- E

**Q25: **

The figure shows a set of traffic lights suspended by two wires attached to posts at the
sides of the road. The left wire makes an angle of
above the horizontal and
carries a tension of 125 N. The left post
is a 14.0 m tall hollow aluminum pole and
is equivalent in strength to a 6.50 cm
diameter solid cylinder. The Young’s modulus of aluminum is N/m^{2} and the shear
modulus is N/m^{2}.

How far is the left post bent to the side?

- A m
- B m
- C m
- D m
- E m

By how much is the left post compressed?

- A m
- B m
- C m
- D m
- E m