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

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

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

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

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

$$411\,J \times 600 = 2.47 \times 10^5$\,J$$

Q: Given that muscle efficiency is less than 20%, how much energy from food is needed to perform $$2.47 \times 10^5$\,J of $$work?

$$E = \frac{2.47 \times 10^5$}{0.2} = 1.235 \times 10^6$\,J$$

Q: If the coefficient of kinetic friction $$\mu_k$$ between rubber and dry concrete is 0.7, what is the kinetic frictional force for a 100 N object sliding on this surface?

$$F_f = \mu_k F_n = 0.7 \times 100 = 70\,N$$

Question 1

Which equation correctly expresses the frictional force $$F_f$$ acting between two surfaces?

Accepted Answer

$$F_f = \mu F_n$$

Question 2

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

Accepted Answer

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

Question 3

During walking, why is the force on the hip joint greater than the person's weight?

Accepted Answer

Because the center of gravity is not directly above the joint, resulting in a force about 2.4 times the weight.

Question 4

Which of the following best describes the role of synovial fluid in joint motion?

Accepted Answer

It lubricates the contact areas, reducing frictional wear at the joints.

Question 5

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

Accepted Answer

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

Question 6

If a person jumps once every second for 10 minutes, what is the total muscle work performed?

Accepted Answer

$$411\,J 	imes 600 = 2.47 	imes 10^5$\,J$$

Question 7

Given that muscle efficiency is less than 20%, how much energy from food is needed to perform $$2.47 	imes 10^5$\,J of $$work?

Accepted Answer

$$E = \frac{2.47 	imes 10^5$}{0.2} = 1.235 	imes 10^6$\,J$$

Question 8

Which formula gives the average velocity $$v_{av}$$ during a time interval $$t$$ for uniform acceleration?

Accepted Answer

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

Question 9

A person stands on an incline. Which condition must be met to prevent sliding?

Accepted Answer

$$F_p \leq F_f$$

Question 10

Which equation describes the distance $$S$$ traversed under uniform acceleration?

Accepted Answer

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

Question 11

During a vertical jump, what is the net upward force acting on the jumper?

Accepted Answer

$$F - W$$

Question 12

What is the formula for the maximum height $$H$$ reached by a jumper, given the reaction force $$F$$, weight $$W$$, and acceleration distance $$c$$?

Accepted Answer

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

Question 13

Which of the following statements about muscle efficiency is correct?

Accepted Answer

Muscle efficiency in converting caloric food energy to work is less than 20%.

Question 14

If the coefficient of kinetic friction $$\mu_k$$ between rubber and dry concrete is 0.7, what is the kinetic frictional force for a 100 N object sliding on this surface?

Accepted Answer

$$F_f = \mu_k F_n = 0.7 	imes 100 = 70\,N$$

Question 15

Which equation relates the final velocity $$v to $$initial velocity $$v_0$$, acceleration $$a$$, and distance $$s$$?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2 a s$

Question 16

A person of weight $$W$$ stands on an incline. The normal force $$F_n is $$given by which equation?

Accepted Answer

$$F_n = W \cos 	heta$$

Question 17

Which of the following best explains why frictional wear at joints is minimized?

Accepted Answer

Smooth cartilage and synovial fluid lubricate the contact areas.

Question 18

A person jumps vertically with a reaction force $$F$$ and weight $$W. $$The acceleration $$a$$ during take-off is given by:

Accepted Answer

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

Question 19

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.

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

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