Q: A person is performing a bicep curl with a 5.0 kg weight held in their hand. The distance from the elbow joint to the hand is 35 cm. What is the torque due to the force of gravity about the elbow joint?

$$\tau = (5.0\ \mathrm{kg})(9.8\ \mathrm{m/s^2$})(0.35\ \mathrm{m}) = 17.15\ \mathrm{N\cdot m}$$

Q: During a bicep curl, the tension $$T in $$the tendon connecting the muscle to the bone is calculated by balancing torques. If the weight exerts a force of $$50\ \mathrm{N} at$$ $$0.35\ \mathrm{m}$$ from the elbow and the tendon acts at $$0.04\ \mathrm{m}$$, what is the tension $$T$$?

$$T = \frac{50\ \mathrm{N} \times 0.35\ \mathrm{m}}{0.04\ \mathrm{m}} = 438\ \mathrm{N}$$

Q: In a free body diagram of the spine, the lower body force acts at $$2/3 of $$the length $$L$$ and the upper body force at $$1/2 of$$ $$L. If $$the reaction force $$R$$ acts at $$30^\circ$$ and the muscle force $$M at$$ $$18^\circ$$, what is the torque equilibrium equation about the end of the spine?

$$\tau_R + \tau_{L_{LB}} + \tau_{L_{UB}} + \tau_M = 0$$

Question 1

A person is performing a bicep curl with a 5.0 kg weight held in their hand. The distance from the elbow joint to the hand is 35 cm. What is the torque due to the force of gravity about the elbow joint?

Accepted Answer

$$	au = (5.0\ \mathrm{kg})(9.8\ \mathrm{m/s^2$})(0.35\ \mathrm{m}) = 17.15\ \mathrm{N\cdot m}$$

Question 2

When analyzing the forces acting on the forearm during a bicep curl, why can the torque due to the forearm's own mass often be ignored?

Accepted Answer

Because the mass of the forearm is much less than the mass being lifted, making its torque negligible.

Question 3

A person is standing on one leg. The muscle tension force $$M$$ acts at an angle of $$70^\circ to $$the horizontal. If the weight of the leg is $$w_{\mathrm{leg}} = 0.16w_p$$, what is the vertical component of the muscle tension force?

Accepted Answer

$$M \sin 70^\circ$$

Question 4

In the context of biomechanical torque, which statement best explains why torques, not forces, are the primary cause of bone fractures?

Accepted Answer

Torques create rotational stresses that can exceed the structural limits of bones, leading to fractures even if the net force is not large.

Question 5

During a bicep curl, the tension $$T in $$the tendon connecting the muscle to the bone is calculated by balancing torques. If the weight exerts a force of $$50\ \mathrm{N} at$$ $$0.35\ \mathrm{m}$$ from the elbow and the tendon acts at $$0.04\ \mathrm{m}$$, what is the tension $$T$$?

Accepted Answer

$$T = \frac{50\ \mathrm{N} 	imes 0.35\ \mathrm{m}}{0.04\ \mathrm{m}} = 438\ \mathrm{N}$$

Question 6

A person stands on one leg. The muscle tension force $$M$$ and the reaction force $$R$$ from the ground act at angles of $$70^\circ$$ and $$0^\circ to $$the horizontal, respectively. Write the equilibrium equation for the $$x-$$direction.

Accepted Answer

$$M \cos 70^\circ - R \cos 0^\circ = 0$$

Question 7

In the analysis of spinal forces, the lower body exerts a force $$F_{\mathrm{lower\ body}} = 0.4w_p$$ and the upper body exerts $$F_{\mathrm{upper\ body}} = 0.2w_p. If $$the reaction force $$R$$ acts at $$30^\circ to $$the horizontal and the muscle force $$M$$ acts at $$18^\circ$$, what is the equilibrium equation for the $$y-$$direction?

Accepted Answer

$$R \sin 30^\circ - M \sin 18^\circ - F_{\mathrm{lower\ body}} - F_{\mathrm{upper\ body}} = 0$$

Question 8

Why is the hip joint particularly vulnerable to fracture in the elderly, according to biomechanical analysis?

Accepted Answer

Because the torque generated by the large force from the pelvis on the femur can exceed the bone's structural limits.

Question 9

A person is standing on one leg. The weight of the leg is $$w_{\mathrm{leg}} = 0.16w_p. If $$the muscle tension force $$M$$ acts at $$70^\circ$$ and the bone contact force $$R$$ acts at $$0^\circ$$, what is the equation for equilibrium in the $$y-$$direction?

Accepted Answer

$$M \sin 70^\circ - R \sin 0^\circ - w_{\mathrm{leg}} = 0$$

Question 10

In a free body diagram of the spine, the lower body force acts at $$2/3 of $$the length $$L$$ and the upper body force at $$1/2 of$$ $$L. If $$the reaction force $$R$$ acts at $$30^\circ$$ and the muscle force $$M at$$ $$18^\circ$$, what is the torque equilibrium equation about the end of the spine?

Accepted Answer

$$	au_R + 	au_{L_{LB}} + 	au_{L_{UB}} + 	au_M = 0$$

Question 11

If the force that the pelvis exerts on the femur can be as great as $$2000\ \mathrm{N}$$, what is the primary biomechanical risk associated with this force?

Accepted Answer

The large torque generated can cause bone fractures, especially in the hip joint.

Question 12

A person is holding a weight in their hand during a bicep curl. If the distance from the elbow to the tendon attachment is $$0.04\ \mathrm{m}$$ and the weight exerts a force of $$50\ \mathrm{N} at$$ $$0.35\ \mathrm{m}$$, which equation correctly relates the torques for static equilibrium?

Accepted Answer

$$T 	imes 0.04\ \mathrm{m} = 50\ \mathrm{N} 	imes 0.35\ \mathrm{m}$$

Question 13

In the analysis of standing on one leg, which of the following best describes the role of the muscle tension force $$M$$?

Accepted Answer

It counteracts the torque produced by the weight of the leg to maintain equilibrium.

Question 14

When constructing a free body diagram for the spine, why is it important to consider both the lower and upper body forces?

Accepted Answer

Because both contribute to the total torque and force that must be balanced for spinal stability.

Question 15

A person is standing on one leg. If the muscle tension force $$M$$ acts at $$70^\circ$$ and the bone contact force $$R$$ acts at $$0^\circ$$, which equation would you use to solve for $$M in $$terms of the person's weight $$w_p$$?

Accepted Answer

$$M (0.07\ \mathrm{m}) \sin 70^\circ + (0.16w_p)(3.2\ \mathrm{cm}) = 0$$

Question 16

In a scenario where a person is standing on one leg, which of the following is a correct expression for the magnitude of the net force $$|\vec{n}| in $$terms of the person's weight $$w_p$$?

Accepted Answer

$$|\vec{n}| = |w_p|$$

Biomechanical Torque and Stability in the Human Body

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