Q: A cylindrical rod of length $$0.500\ \mathrm{m}$$ and diameter $$0.0200\ \mathrm{m} is $$stretched to $$0.501\ \mathrm{m} by a $$force of $$3000\ \mathrm{N}. $$What is the Young's modulus of the material?

$$1.2 \times 10^9$\ \mathrm{N/m^2$}$$

Question 1

A 100-kg block is released from rest and falls 1.0 m in 0.53 s, as shown in the Atwood machine diagram. Assuming the pulley and rope are massless and frictionless, what is the mass $$m of $$the block on the left? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$13\ \mathrm{kg}$$

Question 2

A guitar string is stretched by forces at its ends, a diver is squeezed by water pressure, and a ribbon is deformed by scissors. Which types of stress are represented by these three scenarios, respectively?

Accepted Answer

Tensile, Bulk, Shear

Question 3

According to Hooke's Law, what is the force required to stretch a spring a distance $$x$$ from equilibrium?

Accepted Answer

$$F = kx$$

Question 4

The area under the force vs. displacement graph for a spring represents the work done to stretch the spring. What is the formula for this work?

Accepted Answer

$$W = \frac{1}{2}kX^2$

Question 5

A 0.50 kg mass stretches a spring by 20 cm. If two identical springs are placed in series, how far will the same mass stretch the combined springs?

Accepted Answer

40 cm

Question 6

A 0.50 kg mass stretches a spring by 20 cm. If two identical springs are placed in parallel, how far will the same mass stretch the combined springs?

Accepted Answer

10 cm

Question 7

Which equation correctly defines Young's modulus $$Y$$ for a material under tensile stress?

Accepted Answer

$$Y = \frac{F/A}{\Delta l / l_0$}$$

Question 8

A 1.00-m long wire with a diameter of 0.020 m stretches by 0.030 m when a 20,000-N force is applied. If an identical wire with a diameter of 0.040 m is used, how much will it stretch under the same force?

Accepted Answer

0.0075 m

Question 9

If a metal wire has its length doubled and its diameter tripled, by what factor does its Young's modulus change?

Accepted Answer

No change

Question 10

A cylindrical rod of length $$0.500\ \mathrm{m}$$ and diameter $$0.0200\ \mathrm{m} is $$stretched to $$0.501\ \mathrm{m} by a $$force of $$3000\ \mathrm{N}. $$What is the Young's modulus of the material?

Accepted Answer

$$1.2 	imes 10^9$\ \mathrm{N/m^2$}$$

Question 11

A 1.00-m long wire with a diameter of 0.020 m stretches by 0.030 m when a 20,000-N force is applied. If an identical wire with a length of 2.00 m is used, how much will it stretch under the same force?

Accepted Answer

0.060 m

Question 12

Which of the following best describes the difference between elastic and plastic deformation in a stress-strain diagram?

Accepted Answer

Elastic deformation is reversible, while plastic deformation is permanent.

Question 13

A car is parked on a slope. Under what condition will the car remain in equilibrium?

Accepted Answer

The center of gravity is above the area of support.

Question 14

Which equation represents the first condition for equilibrium for a rigid body?

Accepted Answer

$$\sum \vec{F} = 0$$

Question 15

Which equation represents the second condition for equilibrium for a rigid body?

Accepted Answer

$$\sum \vec{	au} = 0$$

Question 16

A block is acted on by a force at a distance $$r$$ from a pivot point, making an angle $$\phi$$ with the lever arm. Which formula gives the torque $$	au$$?

Accepted Answer

$$	au = rF \sin \phi$$

Question 17

A steel rod is subjected to a force that causes it to stretch. If the stress exceeds the breaking stress listed in Table 11.3, what will happen?

Accepted Answer

The rod will fracture.

Question 18

Which modulus describes a material's resistance to uniform compression?

Accepted Answer

Bulk modulus

Question 19

A diver experiences a force from all sides due to water pressure. What type of stress is this?

Accepted Answer

Bulk stress

Equilibrium & Elasticity: Statics, Stress, Strain, and Moduli

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