Mathematical Homework Assignment for Lecture 05 For all your answers, please write down your calculations and explain your reasoning. Draw sketches whenever helpful, and please use your units correctly. If you are using any online resources (such as unit conversion tools) give their URL and webpage title in your answers.
[a] You are about to lift a small child off the ground. This child weighs Z pounds. How many newtons of gravitational force downward does this child produce?
[b] Use a ruler to measure, to the nearest centimeter, the distance from: The center of your hand to your elbow. Let’s call this distance r,. Your elbow to your shoulder. Let’s call this distance r2. Your shoulder to your lower back (spine). Let’s call this distance r3.
[c] If you lift the child up off the ground, you will experience a moment of force — that is, a torque — on the set of joints from your hand to your spine. Draw a simple sketch (a stick figure is fine) of the physical system where you lift the child with your outstretched arms bent over at your waist, and compute the torque (in units of newton meters, or N m) at your elbow (distance r,), at your shoulder (r, + r2), and at your spine (r, + r2+ r3).
[d] A set of small muscles are attached to your spine at a distance of about 2 inches (0.05 m) from the spine itself. Those muscles must exert force to balance the torque you experience when lifting the child. How much force will those back muscles experience? How many times more force is that than the actual weight of the child?
[e] If, rather than bending at the waist with outstretched arms, you instead stand close to the child, bend at the knees, and lift by straightening your legs while keeping your back close to vertical, how much force will those back muscles experience? Draw a sketch of this physical system to show where the torques would be. What do you think would be the health advantages or disadvantages of this lifting method?
