## Understanding Hip Stabilization through the Gluteus Medius Muscle The stability of the hip is partially maintained by the gluteus medius muscle. The diagrams below aid in understanding this concept: ### Diagram Descriptions: **Figure (a):** - Illustrates a person standing on one leg. - The hip is depicted as an inverted trapezoid. - The femur is represented by two line segments for the neck and shaft. - A single red line denotes the hip muscle. **Figure (b):** - Shows force components with a vector for body weight (W) and another for muscle force (M). - The hip muscle appears prominently in red. **Figure (c):** - Demonstrates weight and muscle forces as a simple lever. - The ball-and-socket joint serves as the pivot. ### Problem-Solving Context: **Given:** 1. Standing on one leg results in 5/6 of a person's weight distributed at the body's center of mass. 2. The leg on which the person balances contributes 1/6 of the mass, hence not affecting torque. 3. Person's total mass: 89 kg. 4. Distance from muscle force (M) to pivot: 7 cm. 5. Distance from weight force (W) to pivot: 15 cm. **Task (a):** Calculate the force exerted by the gluteus medius (M) to maintain hip level. - **Enter the magnitude of force (M) in Newtons.** **Task (b):** Determine the magnitude of the joint reaction force at the pivot. ### Calculation Steps: 1. Convert weight to Newtons (assuming \(g = 9.81 \, \text{m/s}^2\)). 2. Apply torque equilibrium principles around the pivot for solving forces. Assumptions: - All values are accurate to two significant figures. **Problem** a) When standing on one leg, 5/6 of a person's weight is applied at the body's center of mass, as shown in the diagram. The other 1/6 is the mass of the leg on which the person is balancing; therefore, that part of the mass does not affect the torque. If a person's total mass is 89 kg, then what magnitude of force (in Newtons) must the gluteus medius provide to keep the hips level? Assume the distance from M to the pivot is 7 cm and the distance from W to the pivot is 15 cm. Assume all quantities are correct to 2 significant figures. *Enter to 2 significant figures* \( M = \_\_\_\_\_\_\_\_\_\_\_\_\_ \, \text{N} \) b) Calculate the magnitude of the joint reaction force at the pivot. *Enter to 2 significant figures* \( J = \_\_\_\_\_\_\_\_\_\_\_\_\_ \, \text{N} \) c) If the gluteus medius is weak, what effect might that have on the hip when a person stands on one leg? - A. The muscle may not support the weight and the person may lose balance - B. Other muscles might have to support the weight more causing increased strain or pain. - C. Choices A. and B. **Explanation of Diagram** - The diagram illustrates a simplified representation of a person standing on one leg. It shows the distribution of weight with vectors indicating forces applied at specific points. - One vector, labeled W (representing weight), points downwards from a point 15 cm from the pivot, indicating where the weight is applied. - Another vector, labeled M (representing muscle force), points upwards from a point 7 cm from the pivot, illustrating the force exerted by the gluteus medius muscle.