Q: A person holds a weight in their hand with the forearm horizontal. If the muscle force $$F_m$$ acts at an angle $$\theta$$ and the reaction force at the fulcrum $$F_r$$ acts at angle $$\phi$$, which equation represents the balance of forces in the $$x-$$direction?

$$F_m \cos \theta = F_r \cos \phi$$

Q: In the 'weight in hand' scenario, which equation represents the balance of torques about the elbow joint?

$$4 \times F_m \sin \theta = 40 \times W$$

Question 1

Which of the following conditions must be satisfied for a body to be in static equilibrium?

Accepted Answer

Both the vector sum of all forces and the vector sum of all torques acting on the body are zero.

Question 2

A person with mass $$m = 70\ \mathrm{kg}$$ stands upright. What is the magnitude of the gravitational force acting on the person?

Accepted Answer

$$686\ \mathrm{N}$$

Question 3

A body is in stable equilibrium under gravity if:

Accepted Answer

Its center of mass is directly above its base of support.

Question 4

In the context of human balance, what is the primary requirement for maintaining equilibrium while standing?

Accepted Answer

Keeping the center of gravity above the feet.

Question 5

A person with mass $$m = 70\ \mathrm{kg}$$ requires an applied force $$F_a to $$topple. If the torque arm for $$F_a is$$ $$1.5\ \mathrm{m}$$ and for weight is $$0.1\ \mathrm{m}$$, what is the minimum $$F_a$$ needed to topple the person?

Accepted Answer

$$45.7\ \mathrm{N}$$

Question 6

Which equation correctly expresses the torque $$T$$ produced by a force $$F$$ applied at a distance $$r$$ from the pivot?

Accepted Answer

$$T = F 	imes r$$

Question 7

For a lever, the force $$F$$ required to balance a load of weight $$W is $$given by:

Accepted Answer

$$F = \dfrac{W d_1$}{d_2$}$$

Question 8

In a lever system, if $$d_1 is $$the distance from the fulcrum to the load and $$d_2 is $$the distance from the fulcrum to the applied force, what is the mechanical advantage $$M$$?

Accepted Answer

$$M = \dfrac{W}{F} = \dfrac{d_2$}{d_1$}$$

Question 9

A person holds a weight in their hand with the forearm horizontal. If the muscle force $$F_m$$ acts at an angle $$	heta$$ and the reaction force at the fulcrum $$F_r$$ acts at angle $$\phi$$, which equation represents the balance of forces in the $$x-$$direction?

Accepted Answer

$$F_m \cos 	heta = F_r \cos \phi$$

Question 10

In the 'weight in hand' scenario, which equation represents the balance of torques about the elbow joint?

Accepted Answer

$$4 	imes F_m \sin 	heta = 40 	imes W$$

Question 11

If the angle $$	heta is$$ $$72.6^\circ$$ and the mass $$m = 14\ \mathrm{kg}$$, what is the weight $$W$$ acting downward at the hand?

Accepted Answer

$$W = 137.2\ \mathrm{N}$$

Question 12

Which of the following best describes the role of the center of mass in human stability?

Accepted Answer

The center of mass must be maintained above the base of support to ensure stability.

Question 13

A person is carrying a heavy suitcase in one hand. To maintain balance, what must the person do?

Accepted Answer

Shift their center of gravity above their feet.

Question 14

Which class of lever has the fulcrum located between the applied force and the load?

Accepted Answer

First class lever

Question 15

In a third class lever, which of the following is true?

Accepted Answer

The applied force is between the fulcrum and the load.

Question 16

If a person increases the width of their stance, what happens to their stability?

Accepted Answer

Stability increases because the base of support is larger.

Question 17

Which equation represents the balance of forces in the vertical direction for the 'weight in hand' scenario?

Accepted Answer

$$F_m \sin 	heta = W + F_r \sin \phi$$

Question 18

A person is standing on one leg. What must be true for them to remain balanced?

Accepted Answer

Their center of gravity must be above the supporting foot.

Static Equilibrium and Biomechanics: Stability, Levers, and Forces in the Human Body

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