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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.
-During Experiment 2, the subject lifts a ball with a mass m a vertical distance d₁ and then lowers the ball a greater vertical distance d₂. What is the net work done by gravity on the ball?

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.
-During Experiment 2, the subject lifts a ball with a mass m a vertical distance d₁ and then lowers the ball a greater vertical distance d₂. What is the net work done by gravity on the ball?

Quizplus · Accepted Answer

11ecba2d_12d5_8376_a3bf_63acfb1e7d03_MD0008_00 Gravity is a conservative force; it depends on the initial and final position of the mass it acts on. The net work W done by a conservative force is the amount of energy transferred by the force F over a displacement d in the direction of the force: W = Fd Work and displacement are positive if they are in the same direction as the force, and gravity does work only along the vertical axis; W is positive when the ball is lowered because gravity acts downward. The ball's net downward displacement is the difference between the lowered distance d₂ and the raised distance d₁: d = d₂ − d₁ W = F(d₂ − d₁) The force due to gravity on the ball is its weight, which is the product of its mass m and the acceleration due to gravity g: F = mg. Therefore, the net work done by gravity is W = mg(d₂ − d₁) (Choice A) Although the statement "gravity is a conservative force" is accurate, the work done by gravity is not always zero. W = 0 if and only if there is no net displacement in the vertical direction. (Choice C) The expression mgd₂ is the positive work gravity does to lower the ball. However, gravity also does negative work (−mgd₁) when the ball is lifted. Work is negative if the force opposes the object's motion. (Choice D) Although the statement "gravity does work only on the net vertical path" is accurate, the expression mg(d₁ + d₂) is not the net displacement of the ball but the total distance traveled. Educational objective: Gravity is a conservative force, and the work W done by a conservative force F over a displacement d is W = Fd, where d is in the same direction as the force. The force due to gravity (weight) is the product of mass m and gravitational acceleration g.

Passage The Humerus Bone in the Upper Arm and the Radius