# Explanation of the for Each Part ## (a) Magnitude of the Force \( F_B \) in the Back Muscles **Theory:** - The force \( F_B \) in the back muscles must support the weight of both the body and the box. - This a static equilibrium problem, where the of forces and the sum of momentstorques) be zero. - The main idea is to calculate the moment due to the weights of the upper body and the box, and then determine the muscular force \( F_B \) required at the pivot point to counteract these moments. - The vertical distances (perpendicular distances from the pivot to the line of action of forces) are crucial in calculating moments. **Calculation:** - Use the principle of moments about the pivot point: \[ \sum \tau = \Rightarrow F_B \times \text{vertical distance} = \text{sum of moments due to weights} \] - The weights act vertically downward at their respective centers of mass. - The moments are calculated as: \[ \text{Moment} = \text{force} \times \text{distance from pivot} \] ## (b) Magnitude and Direction of the Force \( F_v \) on the Spine **Theory:** - The force \( F_v \) is the vertical component of the force exerted by the vertebrae on the spine due to the load. - It acts along the spine, at an angle \( \theta \) to the vertical. - The force can be found by analyzing the equilibrium of forces in the vertical and horizontal directions, considering the components of \( F_v \) and the muscular forces. - The direction (angle \( \theta \)) indicates how the vertebrae are supporting the load at an inclined angle. **Calculation:** - Resolve the total load into components along and perpendicular to the spine. - Use trigonometric relations to find \( F_v \): \[ F_v = \frac{\text{total load}}{\cos \theta} \] - The total load includes the weight of the upper body, the box, and the muscular support. --- ## Additional Notes: - The distances (35 cm, 50 cm, 8 cm) and angles (29°, 39°, 61°, 10°) are used to resolve forces and moments accurately. - Gravity \( g = 9.81\, \text{m/s}^2 \) converts mass to weight (force). --- This theoretical framework helps in understanding how the forces are distributed in the body during lifting and how to calculate the muscular and vertebral forces involved.