HPP Activity A25.v1 Static Equilibrium Exploration GE 1. Sit upright with head held straight. Now bend your head forward and hold it steady. 1. What do you feel in your neck as you keep your head steady in this tilted position? 2. What do you think would happen to the upright head if no neck muscle exerts a torque about the atlanto-occipital joint, where the skull attaches to the cervical vertebrae? 3. Explain why your head falls forward when you fall asleep in class. 4. What torques do you think act about the atlanto-occipital joint? 5. How should the sign of the muscle torque compare with the sign of the skull weight torque? Invention To keep a mechanical system in static equilibrium, two conditions must be realized: 1. The net external force on the system must be zero. 2. The net external torque on the system, about any axis, must be zero. Using equations, these conditions are expressed as One way to think about the torque equation is to say that the torques must balance. This occurs if the lever involved does not rotate. Application Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity A25.v1 2 Have one student in your group positioned with their hand on a door close to the hinge. Have another student, positioned on the opposite side of the door on the edge furthest from the hinge, with just one finger on the door. The student close to the hinge will try to push the door closed as hard as he can, while the other student will try to oppose him. If the door doesn't move - the torques must balance. GE 2. 1. Compare the relative amounts of force the students exert on the door. 2. Can you explain any differences? 3. Describe how the conditions for static equilibrium apply to this situation. Application Obtain an experimental beam/fulcrum system on which masses can be hung.
HPP Activity A25.v1 3 GE 3. Start with the fulcrum in the center as shown. Hang equal masses on each end so that the system is balanced. Call these weights F L and F R. Let the distance of each mass to the fulcrum be represented by r L and r R. 1. Note the values of F L, F R, r L, and r R. 2. Choose two additional values of r R, and find the required F R to balance the beam. Complete the data table. F L [N] r L [m] τ L [Nm] F R [N] r L [m] τ R [Nm] 3. Does your data support the required conditions for static equilibrium? Application In this application, you will complete the described procedure to answer the following question: What is the force exerted by the biceps to keep the lower part of your arm level with your upper arm perpendicular to the lower arm while holding a significant amount of weight? GE 4. Procedure: 1. Locate the pivot point for the subject's lower arm and where the biceps connect to the lower arm. Determine the point where the biceps attach. Estimate the relevant distances from the pivot for this person's arm (such as the distance to the place where the muscles connect and the distance to the center of mass) 2. Hang a substantial amount of weight from your hand. Don't hurt yourself! Estimate and record the weight of the subject's lower arm (using the provided chart- below). Also record the weight and location from the pivot point, of the weight(s) hanging from your hand.
HPP Activity A25.v1 4 ratios from a 1969 cadaver study Head 7.3 % Trunk 50.7 % Upper arm 2.6 % Forearm 1.6 % Hand 0.7 % Total Arm 4.9 % Forearm and hand 2.3 % Thigh 10.3 % Calf 4.3 % Foot 1.5 % Total leg 16.1 % Calf and foot 5.8 % 3. Carefully sketch the free-body diagram of the lower arm, including the force of the biceps muscle and any other relevant forces. Record all of your distance and weight measurements on this drawing. Don't forget any of the forces! Ask your instructor to check your drawing.
HPP Activity A25.v1 5 4. Using the ideas of static equilibrium and net torque, what is the force (in N and lbs) exerted by the subject's biceps on the arm? Show all necessary calculations. 5. Using the equation for net force on the lower arm, determine the force exerted on the lower arm by the upper arm bone (at the elbow). 6. Compare these numbers to the subject's body weight. Application Level Arm: Pushing Down (Triceps calculation)
HPP Activity A25.v1 6 What is the maximum weight that you can push down with your hand if you keep the lower part of your arm level and your upper arm perpendicular to the lower arm? 1. Locate the pivot point for the same subject's arm and where his/her triceps connects to the lower arm. Estimate the necessary distances and angles. Record the values below. 2. Push down on the scale with as much force as you can while keeping your forearm level. No fair leaning on the scale! Record the value here. 3. Sketch the upper arm/lower arm system, including the triceps muscle. Record the maximum push, all other measurements. 4. Setting the sum of all the torques equal to zero, solve the resulting equation for the force (in N and lbs) exerted by your triceps on the lower arm. Compare this number to your total body weight and to the force exerted by your biceps when lifting a heavy weight. Which muscle needs to be the stronger? 5. Using the equation for net force on the lower arm, determine the force exerted on the lower arm by the upper arm bone (at the elbow). How does this force compare to other forces in the arm?