Q: A person of weight $W$ stands on an oak board inclined at angle $\theta$. If the static coefficient of friction is $\mu_s = 0.6$, what is the maximum angle $\theta$ before the person begins to slide?

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

Q: A 70 kg person jumps up to a height of 0.6 m once every second for 10 minutes. If muscle efficiency is 20%, what is the total energy required from food to perform this activity?

$E = \frac{70 \times 9.8 \times 0.6 \times 600}{0.2} \approx 123,000 \text{ J}$

Q: A steel block slides on ice. If the static coefficient of friction is $\mu_s = 0.02$ and the normal force is $100$ N, what is the maximum static friction force?

$F_{f,\text{max}} = 0.02 \times 100 = 2 \text{ N}$

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

$W \sin \theta \leq \mu_s W \cos \theta$

Question 1

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 2

A person of weight $W$ stands on an oak board inclined at angle $	heta$. If the static coefficient of friction is $\mu_s = 0.6$, what is the maximum angle $	heta$ before the person begins to slide?

Accepted Answer

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

Question 3

Which of the following surfaces has the lowest kinetic coefficient of friction according to the provided data?

Accepted Answer

Bone on joint, lubricated

Question 4

When a person walks, 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 larger force due to leverage.

Question 5

A 70 kg person jumps up to a height of 0.6 m once every second for 10 minutes. If muscle efficiency is 20%, what is the total energy required from food to perform this activity?

Accepted Answer

$E = \frac{70 	imes 9.8 	imes 0.6 	imes 600}{0.2} \approx 123,000 	ext{ J}$

Question 6

Which factor most effectively reduces frictional wear at the hip joint during walking?

Accepted Answer

Presence of smooth cartilage and synovial fluid

Question 7

For an object moving with uniform acceleration $a$, which equation gives the distance $s$ traversed after time $t$ starting from initial velocity $v_0$?

Accepted Answer

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

Question 8

A steel block slides on ice. If the static coefficient of friction is $\mu_s = 0.02$ and the normal force is $100$ N, what is the maximum static friction force?

Accepted Answer

$F_{f,	ext{max}} = 0.02 	imes 100 = 2 	ext{ N}$

Question 9

Which equation correctly relates the final velocity $v$ to the initial velocity $v_0$, acceleration $a$, and distance $s$ for an object under uniform acceleration?

Accepted Answer

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

Question 10

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

Accepted Answer

$W \sin 	heta \leq \mu_s W \cos 	heta$

Question 11

During walking, the force on the hip joint can be up to how many times the body weight?

Accepted Answer

About 5 times the body weight

Question 12

Which of the following best describes kinetic friction?

Accepted Answer

The frictional force acting on a moving object, proportional to $\mu_k$

Question 13

If a person of weight $W$ stands on a surface with coefficient of static friction $\mu_s$, what is the maximum horizontal force that can be applied before the person starts sliding?

Accepted Answer

$F_{	ext{max}} = \mu_s W$

Question 14

Which of the following statements about muscle efficiency in converting food energy to work is correct?

Accepted Answer

Muscle efficiency is less than 20%

Question 15

A person jumps vertically with a take-off velocity $v_0$. What is the maximum height $H$ reached, neglecting air resistance?

Accepted Answer

$H = \frac{v_0^2}{2g}$

Question 16

Which of the following is NOT a method by which the body reduces frictional wear at the joints?

Accepted Answer

Increasing the roughness of cartilage

Question 17

If the net upward force on a jumper is $F - W$ and the acceleration occurs over a distance $c$, what is the take-off velocity $v$?

Accepted Answer

$v = \sqrt{2(F - W)c / m}$

Question 18

Which equation gives the average velocity $v_{av}$ during a time interval $t$ for an object accelerating uniformly from $v_0$ to $v$?

Accepted Answer

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

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

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