Q: A person is holding a weight in their hand with the forearm horizontal. If the muscle force $$F_m$$ acts at an angle $$\theta to $$the forearm, which equation correctly represents the balance of torques about the elbow joint?

$$F_m \sin \theta \times d_m = W \times d_w$$

Q: In the 'weight in hand' scenario, which equation represents the balance of vertical forces?

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

Q: A person is holding a 14 kg mass in their hand with the forearm at an angle $$\theta = 72.6^\circ. If $$the torque equation is $$4 F_m \sin \theta = 40 W$$, what is the value of $$F_m$$? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$F_m = \dfrac{40 \times 14 \times 9.8}{4 \times \sin 72.6^\circ}$$

Q: Which equation correctly expresses the balance of horizontal forces in the 'weight in hand' scenario?

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

Question 1

Which of the following statements best describes the condition for a body to be in static equilibrium?

Accepted Answer

Both the vectorial sum of the forces and the torques acting on the body must be zero.

Question 2

A person with mass $$m = 70\ \mathrm{kg}$$ stands upright. If the distance from the point of applied force to the pivot is $$1.5\ \mathrm{m}$$ and the distance from the center of mass to the pivot is $$0.1\ \mathrm{m}$$, what is the minimum force $$F_a$$ required to topple the person? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_a = 45.7\ \mathrm{N}$$

Question 3

Which of the following best explains why a person is more stable when standing with feet apart?

Accepted Answer

The base of support is increased, making it easier to keep the center of mass above the base.

Question 4

A lever is used to lift a load of weight $$W. If $$the distance from the fulcrum to the load is $$d_1$$ and the distance from the fulcrum to the applied force is $$d_2$$, what is the force $$F$$ required to balance the load?

Accepted Answer

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

Question 5

In the context of human balance, what is the most critical factor for maintaining equilibrium while standing?

Accepted Answer

Maintaining the center of gravity directly above the feet.

Question 6

A person is holding a weight in their hand with the forearm horizontal. If the muscle force $$F_m$$ acts at an angle $$	heta to $$the forearm, which equation correctly represents the balance of torques about the elbow joint?

Accepted Answer

$$F_m \sin 	heta 	imes d_m = W 	imes d_w$$

Question 7

Which of the following is NOT a characteristic of a body in stable equilibrium under gravity?

Accepted Answer

A small displacement lowers the center of mass.

Question 8

A lever has $$d_1 = 0.5$$\ \mathrm{m}$$ and d_2$ = 2.0\ \mathrm{m}. If $$the load is $$W = 100\ \mathrm{N}$$, what is the mechanical advantage $$M of $$the lever?

Accepted Answer

$$M = \dfrac{d_2$}{d_1$} = 4$$

Question 9

In the 'weight in hand' scenario, which equation represents the balance of vertical forces?

Accepted Answer

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

Question 10

A person is holding a 14 kg mass in their hand with the forearm at an angle $$	heta = 72.6^\circ. If $$the torque equation is $$4 F_m \sin 	heta = 40 W$$, what is the value of $$F_m$$? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_m = \dfrac{40 	imes 14 	imes 9.8}{4 	imes \sin 72.6^\circ}$$

Question 11

Which of the following best describes the function of the human arm when holding a weight as shown in the 'weight in hand' example?

Accepted Answer

It acts as a third-class lever, with the muscle force applied between the fulcrum and the load.

Question 12

If a body is in unstable equilibrium, what happens when it is slightly displaced?

Accepted Answer

It moves further away from its original position.

Question 13

Which equation correctly expresses the balance of horizontal forces in the 'weight in hand' scenario?

Accepted Answer

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

Question 14

A person is carrying a heavy suitcase in one hand. Which of the following strategies will help them maintain equilibrium?

Accepted Answer

Leaning away from the suitcase to keep the center of gravity above the feet.

Question 15

Which of the following is true about the mechanical advantage $$M of a $$lever?

Accepted Answer

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

Question 16

Which of the following best describes the effect of increasing the distance $$d_2 ($$from fulcrum to applied force) in a lever system?

Accepted Answer

It decreases the force required to balance the load.

Question 17

A person with mass $$m is $$standing. If the center of mass is not above the base of support, what is most likely to happen?

Accepted Answer

The person will topple over.

Question 18

Which of the following is a correct statement about the balance of torques for a body in equilibrium?

Accepted Answer

The sum of all torques about any axis must be zero.

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

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