Passage
The humerus bone in the upper arm and the radius bone in the lower arm can be modeled as a lever with the elbow joint as the pivot point. Movement about the elbow results from a combination of internal and external forces acting on these bones. The primary internal force is generated from contractions of skeletal muscles; a 1-cm² cross-sectional area of skeletal muscle can generate a maximum of 7 × 10⁶ dynes of force (1 dyn = 1 g⋅cm/s²) . Friction between the humerus and the radius at the elbow is another internal force that can affect arm movements. As people age, cartilage degeneration decreases the lubrication between bones, which increases the coefficients of static and kinetic friction.The contraction of the biceps, a skeletal muscle in the upper arm, exerts a pulling force on the radius in the lower arm. If the torque generated by this muscle exceeds that of any opposing internal and external forces, the arm curls about the elbow. This specific type of movement is known as a concentric muscle contraction.The following experiments were performed with a 30-year-old male subject. Electrodes were placed around the subject's biceps and attached to an electromyograph, a device that measures the electrical activity of skeletal muscle contractions. The estimated weight of the subject's lower arm is 45 N, and the subject's lower arm segments to the elbow are shown in Table 1.Table 1 Lower Arm Segment Lengths
Experiment 1The subject kept his entire arm stationary and in a fixed position while holding balls of varying masses. The upper arm was perpendicular to the ground, and the lower arm was parallel to the ground (Figure 1) .
Figure 1 The fixed position of the arm during Experiment 1Experiment 2The subject kept his upper arm stationary and perpendicular to the ground while lifting and lowering balls of varying masses.
Adapted from N. Ozkaya, Fundamentals of Biomechanics. (C) 2016 Springer.
-Ignoring the weight of the arm, what is the mechanical advantage of the biceps when it is lifting a ball in Experiment 2?

Question

Passage
The humerus bone in the upper arm and the radius bone in the lower arm can be modeled as a lever with the elbow joint as the pivot point. Movement about the elbow results from a combination of internal and external forces acting on these bones. The primary internal force is generated from contractions of skeletal muscles; a 1-cm² cross-sectional area of skeletal muscle can generate a maximum of 7 × 10⁶ dynes of force (1 dyn = 1 g⋅cm/s²) . Friction between the humerus and the radius at the elbow is another internal force that can affect arm movements. As people age, cartilage degeneration decreases the lubrication between bones, which increases the coefficients of static and kinetic friction.The contraction of the biceps, a skeletal muscle in the upper arm, exerts a pulling force on the radius in the lower arm. If the torque generated by this muscle exceeds that of any opposing internal and external forces, the arm curls about the elbow. This specific type of movement is known as a concentric muscle contraction.The following experiments were performed with a 30-year-old male subject. Electrodes were placed around the subject's biceps and attached to an electromyograph, a device that measures the electrical activity of skeletal muscle contractions. The estimated weight of the subject's lower arm is 45 N, and the subject's lower arm segments to the elbow are shown in Table 1.Table 1 Lower Arm Segment Lengths

Experiment 1The subject kept his entire arm stationary and in a fixed position while holding balls of varying masses. The upper arm was perpendicular to the ground, and the lower arm was parallel to the ground (Figure 1) .

Figure 1 The fixed position of the arm during Experiment 1Experiment 2The subject kept his upper arm stationary and perpendicular to the ground while lifting and lowering balls of varying masses.
Adapted from N. Ozkaya, Fundamentals of Biomechanics. (C) 2016 Springer.
-Ignoring the weight of the arm, what is the mechanical advantage of the biceps when it is lifting a ball in Experiment 2?

Quizplus · Accepted Answer

11ecba2d_12d7_f488_a3bf_71f2d002f42f_MD0008_00 According to the passage, the arm is modeled as a lever with the pivot point (fulcrum) at the elbow. Mechanical advantage is the ratio of the output force F_o to the input force F_i: 11ecba2d_12d7_f489_a3bf_d15f70ceb50f_MD0008_00 Work W is the amount of energy transferred by a force F over a distance d: W = Fd. A simple machine can amplify an input force through the conservation of energy; eg, a lever can transfer small forces over long distances into large forces over short distances. The work done by the output force must equal the work done by the input force: 11ecba2d_12d8_1b9a_a3bf_33a38234d0fd_MD0008_00 where d_i and d_o are the distances from the pivot point to the input and output forces, respectively. These distances can be used in place of the vertical displacements of the forces due to the geometry of a lever. Rearranging the above equation, the mechanical advantage of a lever is equal to the ratio of the input distance to the output distance: 11ecba2d_12d8_1b9b_a3bf_95ce851a97c8_MD0008_00 mechanical advantage=FoFi = dido The question asks for the mechanical advantage of the subject's biceps in lifting a ball. The input distance d_i is 3 cm to the biceps, and the output distance d_o is 30 cm to the ball. Using these values, the mechanical advantage is 11ecba2d_12d8_1b9c_a3bf_01d1a83a4ffc_MD0008_00 The mechanical advantage of the biceps is <1, which means that a relatively large input force from the biceps is required to balance an opposing force at the hand. (Choices A and D) If the entire length of the arm (45 cm) is incorrectly used as the output distance, the mechanical advantage of the biceps would be calculated as 0.07, and the inverse of this value is 15. (Choice C) The mechanical advantage of ball on the biceps is 10 and is calculated by designating the ball as the input force and the biceps as the output force. Educational objective: The mechanical advantage of a simple machine is the ratio of the output force to the input force. Due to the conservation of energy, the mechanical advantage of a lever is also equal to the ratio of the input distance to the output distance.

Passage The Humerus Bone in the Upper Arm and the Radius