Q: A 70 kg person stands on an oak board inclined at an angle $$\theta. If $$the coefficient of static friction between the shoes and the board is $$\mu_s = 0.6$$, what is the maximum angle $$\theta at $$which the person can stand without sliding down?

$$\theta = \arctan(0.6) \approx 31^\circ$$

Q: During walking, the force exerted on the hip joint is greater than the body weight. If a person weighs 70 kg, what is the approximate force on the hip joint during walking?

$$F_{hip} \approx 2.4 \times 70 \times 9.8 = 1646\,\mathrm{N}$$

Q: A 70 kg person jumps vertically upward to a height of 0.6 m. What is the work done by the muscles in one jump?

$$W = mgh = 70 \times 9.8 \times 0.6 = 411\,\mathrm{J}$$

Q: If a person jumps once every second for 10 minutes, how many jumps are performed and what is the total muscle work done?

600 jumps; $$411 \times 600 = 2.47 \times 10^4$\,\mathrm{J}$$

Q: Given that muscle efficiency in converting food energy to work is 20%, how much energy from food is needed to perform $$2.47 \times 10^4$\,\mathrm{J} of $$muscle work?

$$E_{food} = \dfrac{2.47 \times 10^4$}{0.2} = 1.235 \times 10^5$\,\mathrm{J}$$

Q: If the coefficient of friction between bone and joint (lubricated) is $$\mu = 0.01$$, and the normal force is $$F_n = 1000\,\mathrm{N}$$, what is the frictional force?

$$F_f = 0.01 \times 1000 = 10\,\mathrm{N}$$

Question 1

A 70 kg person stands on an oak board inclined at an angle $$	heta. If $$the coefficient of static friction between the shoes and the board is $$\mu_s = 0.6$$, what is the maximum angle $$	heta at $$which the person can stand without sliding down?

Accepted Answer

$$	heta = \arctan(0.6) \approx 31^\circ$$

Question 2

Which equation correctly expresses the frictional force $$F_f$$ acting on an object pressed against a surface with normal force $$F_n$$ and coefficient of friction $$\mu$$?

Accepted Answer

$$F_f = \mu F_n$$

Question 3

During walking, the force exerted on the hip joint is greater than the body weight. If a person weighs 70 kg, what is the approximate force on the hip joint during walking?

Accepted Answer

$$F_{hip} \approx 2.4 	imes 70 	imes 9.8 = 1646\,\mathrm{N}$$

Question 4

A 70 kg person jumps vertically upward to a height of 0.6 m. What is the work done by the muscles in one jump?

Accepted Answer

$$W = mgh = 70 	imes 9.8 	imes 0.6 = 411\,\mathrm{J}$$

Question 5

If a person jumps once every second for 10 minutes, how many jumps are performed and what is the total muscle work done?

Accepted Answer

600 jumps; $$411 	imes 600 = 2.47 	imes 10^4$\,\mathrm{J}$$

Question 6

Given that muscle efficiency in converting food energy to work is 20%, how much energy from food is needed to perform $$2.47 	imes 10^4$\,\mathrm{J} of $$muscle work?

Accepted Answer

$$E_{food} = \dfrac{2.47 	imes 10^4$}{0.2} = 1.235 	imes 10^5$\,\mathrm{J}$$

Question 7

Which of the following best explains why frictional wear at the hip joint is minimized during walking?

Accepted Answer

The contact ends of the bone are coated with smooth cartilage and lubricated by synovial fluid.

Question 8

A block of mass $$m is $$placed on a horizontal surface. If the coefficient of kinetic friction is $$\mu_k$$, what is the minimum force required to keep the block moving at constant velocity?

Accepted Answer

$$F = \mu_k m g$$

Question 9

Which formula gives the distance $$S$$ traversed by an object under uniform acceleration $$a$$ over time $$t$$, starting from initial velocity $$v_0$$?

Accepted Answer

$$S = v_0$ t + \dfrac{a t^2$}{2}$$

Question 10

During a vertical jump, the net upward force on the jumper is $$F - W. $$What is the acceleration $$a of $$the jumper?

Accepted Answer

$$a = \dfrac{F - W}{m}$$

Question 11

A person of weight $$W$$ stands on an incline at angle $$	heta. $$What is the component of weight parallel to the incline?

Accepted Answer

$$F_p = W \sin 	heta$$

Question 12

If the coefficient of friction between bone and joint (lubricated) is $$\mu = 0.01$$, and the normal force is $$F_n = 1000\,\mathrm{N}$$, what is the frictional force?

Accepted Answer

$$F_f = 0.01 	imes 1000 = 10\,\mathrm{N}$$

Question 13

Which statement about muscle efficiency is correct?

Accepted Answer

Less than 20% of the chemical energy from food is converted to muscle work.

Question 14

A jumper accelerates over a distance $$c$$ before take-off. If the net upward force is $$F - W$$, what is the velocity $$v at $$take-off?

Accepted Answer

$$v^2 = 2c$$ \dfrac{F - W}{W/g}$$

Question 15

Which of the following is true about static and kinetic friction?

Accepted Answer

Static friction ($$\mu_s) is $$generally greater than kinetic friction ($$\mu_k) $$for the same surfaces.

Question 16

A person of weight $$W$$ stands on an incline. The normal force $$F_n$$ acting on the person is:

Accepted Answer

$$F_n = W \cos 	heta$$

Question 17

Which equation gives the average velocity $$v_{av}$$ during a time interval $$t$$ for an object with initial velocity $$v_0$$ and final velocity $$v$$?

Accepted Answer

$$v_{av} = \dfrac{v + v_0$}{2}$$

Question 18

Which of the following best describes the condition for a person to start sliding down an incline?

Accepted Answer

The component of weight parallel to the incline exceeds the maximum static friction force: $$W \sin 	heta \u003e \mu_s W \cos 	heta$$

Question 19

A person jumps vertically upward. At the maximum height $$H$$, which equation relates $$H to $$the net force and acceleration distance $$c$$?

Accepted Answer

$$H = \dfrac{(F - W)c}{W}$$

Biophysics: Friction, Inclines, Translational Motion, and Energy in Physical Activity

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