Q: A skier with a mass of 45 kg is sliding down a snowy slope at an angle of $$25^\ ext{o}. If $$the coefficient of kinetic friction $$\mu_k$$ between the skis and snow is 0.082, what is the magnitude of the frictional force acting on the skier?

$$F_f = \mu_k mg \cos\theta = 0.082 \times 45 \times 9.8 \times \cos(25^\text{o}) \approx 33 N$$

Q: A steel cable with cross-sectional area $$A = 2.4 \times 10$$^{-4}$$ \ \text{m}^2$$ and Young's modulus $$Y = 2.1 \times 10$$^{11}$$ \ \text{N/m}^2$$ stretches by $$\Delta L = 0.18 m $$when supporting a load. If the original length is $$L = 30.2 m$$, what is the tension $$F in $$the cable?

$$F = Y \dfrac{A \Delta L}{L} = 2.1 \times 10$$^{11}$$ \times \dfrac{2.4 \times 10$$^{-4}$$ \times 0.18}{30.2} \approx 3 \times 10^4$ N

Q: A bone under tension has a Young's modulus of $$1.6 \times 10$$^{10}$$ \ \text{N/m}^2. If a $$force of $$1600 N is $$applied to a bone of length $$0.5 m $$and cross-sectional area $$2 \times 10$$^{-4}$$ \ \text{m}^2$$, what is the extension $$\Delta L$$?

$$\Delta L = \dfrac{F L}{A Y} = \dfrac{1600 \times 0.5}{2 \times 10$$^{-4}$$ \times 1.6 \times 10$$^{10}$$} \approx 2.5 \times 10$$^{-4}$$ m

Q: Which of the following best describes the relationship between stress and strain for an elastic material?

Stress is proportional to strain: $$\text{Stress} = Y \times \text{Strain}$$

Q: A nylon rope is stretched with a force of 500 N. If its original length is 2 m, cross-sectional area is $$5 \times 10$$^{-5}$$ \ \text{m}^2$$, and Young's modulus is $$3 \times 10^9$ \ \text{N/m}^2$$, what is the strain in the rope?

$$\text{Strain} = \dfrac{\Delta L}{L} = \dfrac{F}{A Y L} \times L = \dfrac{F}{A Y} = \dfrac{500}{5 \times 10$$^{-5}$$ \times 3 \times 10^9$} \approx 3.3 \times 10$$^{-4}$$

Question 1

A skier with a mass of 45 kg is sliding down a snowy slope at an angle of $$25^\	ext{o}. If $$the coefficient of kinetic friction $$\mu_k$$ between the skis and snow is 0.082, what is the magnitude of the frictional force acting on the skier?

Accepted Answer

$$F_f = \mu_k mg \cos	heta = 0.082 	imes 45 	imes 9.8 	imes \cos(25^	ext{o}) \approx 33 N$$

Question 2

Which statement best describes the difference between static friction and kinetic friction?

Accepted Answer

Static friction prevents motion up to a maximum value, while kinetic friction acts when objects are moving and is usually less than static friction.

Question 3

A steel cable with cross-sectional area $$A = 2.4 	imes 10$$^{-4}$$ \ 	ext{m}^2$$ and Young's modulus $$Y = 2.1 	imes 10$$^{11}$$ \ 	ext{N/m}^2$$ stretches by $$\Delta L = 0.18 m $$when supporting a load. If the original length is $$L = 30.2 m$$, what is the tension $$F in $$the cable?

Accepted Answer

$$F = Y \dfrac{A \Delta L}{L} = 2.1 	imes 10$$^{11}$$ 	imes \dfrac{2.4 	imes 10$$^{-4}$$ 	imes 0.18}{30.2} \approx 3 	imes 10^4$ N

Question 4

Which material listed below has the lowest coefficient of kinetic friction ($$\mu_k) $$according to the study guide?

Accepted Answer

Bone (synovial fluid)

Question 5

If a tendon is stretched by a force $$F$$ and obeys Hooke's Law, which equation correctly relates the force to the extension $$\Delta L$$?

Accepted Answer

$$F = k \Delta L$$

Question 6

A bone under tension has a Young's modulus of $$1.6 	imes 10$$^{10}$$ \ 	ext{N/m}^2. If a $$force of $$1600 N is $$applied to a bone of length $$0.5 m $$and cross-sectional area $$2 	imes 10$$^{-4}$$ \ 	ext{m}^2$$, what is the extension $$\Delta L$$?

Accepted Answer

$$\Delta L = \dfrac{F L}{A Y} = \dfrac{1600 	imes 0.5}{2 	imes 10$$^{-4}$$ 	imes 1.6 	imes 10$$^{10}$$} \approx 2.5 	imes 10$$^{-4}$$ m

Question 7

Why does friction produce heat when two surfaces slide against each other?

Accepted Answer

Friction converts kinetic energy into thermal energy due to microscopic interactions at the surfaces.

Question 8

Which of the following best describes the relationship between stress and strain for an elastic material?

Accepted Answer

Stress is proportional to strain: $$	ext{Stress} = Y 	imes 	ext{Strain}$$

Question 9

A person walking on ice slips more easily than on concrete. Which physical property explains this difference?

Accepted Answer

The coefficient of friction ($$\mu) $$between shoes and ice is much lower than between shoes and concrete.

Question 10

If the normal force $$N$$ between two surfaces is doubled, what happens to the frictional force $$F_f$$ assuming the coefficient of friction $$\mu$$ remains constant?

Accepted Answer

$$F_f$$ doubles because $$F_f = \mu N$$

Question 11

Which material from the study guide is most elastic, based on Young's modulus values?

Accepted Answer

Tendon

Question 12

A box is at rest on a horizontal surface. Which force must be overcome to start moving the box?

Accepted Answer

Static friction

Question 13

If a steel block slides on steel (dry), which coefficient should be used to calculate the frictional force while it is moving?

Accepted Answer

$$\mu_k = 0.3$$

Question 14

A nylon rope is stretched with a force of 500 N. If its original length is 2 m, cross-sectional area is $$5 	imes 10$$^{-5}$$ \ 	ext{m}^2$$, and Young's modulus is $$3 	imes 10^9$ \ 	ext{N/m}^2$$, what is the strain in the rope?

Accepted Answer

$$	ext{Strain} = \dfrac{\Delta L}{L} = \dfrac{F}{A Y L} 	imes L = \dfrac{F}{A Y} = \dfrac{500}{5 	imes 10$$^{-5}$$ 	imes 3 	imes 10^9$} \approx 3.3 	imes 10$$^{-4}$$

Question 15

Which scenario would increase the frictional force between two surfaces?

Accepted Answer

Increasing the normal force pressing the surfaces together

Question 16

A tendon stretches by 1 mm when a force of 10 N is applied. What is the spring constant $$k of $$the tendon?

Accepted Answer

$$k = \dfrac{F}{\Delta L} = \dfrac{10}{0.001} = 10,000 N/m$$

Question 17

Which of the following best explains why synovial fluid in joints results in very low friction?

Accepted Answer

Synovial fluid acts as a lubricant, reducing the coefficient of friction between bone surfaces.

Question 18

A climber hangs from a nylon rope. If the rope stretches by 2 cm under a load of 800 N, what is the effective spring constant $$k of $$the rope?

Accepted Answer

$$k = \dfrac{F}{\Delta L} = \dfrac{800}{0.02} = 40,000 N/m$$

Question 19

Which of the following is NOT a factor that affects the magnitude of friction between two surfaces?

Accepted Answer

The color of the surfaces

Chapter 5 Friction and Elasticity: Key Concepts, Formulas, and Applications

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