How could this be fixed? Observation Experiments in Static Equilibrium
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1 How could this be fixed? Observation Experiments in Static Equilibrium
2 Balance the Meter Stick Predict where you should place your finger in order to balance the meter stick. What assumptions did you make in making your prediction? Does your prediction match the outcome exactly?
3 Balancing the Easy Way Put your fingers on either end of a meter stick and slowly bring them together until they meet. Why does only one finger move at a time? When does one finger stop moving and the other start moving? Check your reasoning with Derek Muller from Veritasium: (1:45-2: 22)
4 Center of Mass The center of mass of an object is a point where a force exerted on the object pointing directly toward or away from that point, will not cause the object to turn.
5 Check for Understanding Imagine you place a board on your desk and you push on it in different directions as pictured. Forces 1 and 3 cause the board to slide, and forces 2 and 4 cause the board to slide and rotate. Find an approximate center of mass.
6 A Qualitative Understanding Balance a meter stick on the stand Place/hang an object anywhere on right side of the stand Place/hang a second object of different mass on the left side of the stand so that the meter stick is balanced Repeat this experiment, this time with three new objects Record the pattern or patterns that you observe
7 Where is the gravitational force exerted? Earth exerts a downward force on every part of an object. Using the definition of center of mass, why can we assume that the total force is exerted exactly at the center of mass?
8 Mass of a Meter Stick Using only your understanding of static equilibrium, a meter stick and one or more objects, determine the mass of a meter stick. Show ALL calculations, diagrams, data, uncertainties, assumptions, and results in your notebook.
9 APPLICATION EXPERIMENT: WHY SHOULDN T YOU LIFT FROM A BENT POSITION? A woman is lifting a 30-lb barbell. A mechanical model of her upper body is shown below the picture. The beam is her backbone and the cable is her back muscles (a complex set of muscles in the real back). The Earth s gravitational force on her upper body at its center of mass is 30 lb. The Earth s gravitational force on her head, arms, and the barbell is 50 lb at the end of the beam. The back muscle (rope) connects 0.20 m from the right end of the 0.60-m long beam (the backbone) and makes a 15 o angle with the beam. Apply the conditions of equilibrium to the beam and use them to estimate the force that one primary back muscle (it is a complex system) exerts on the backbone and the compression of the beam at its joint on the left side. (Each year more than half a million Americans get serious back problems by lifting this way.)
10 APPLICATION EXPERIMENT: WHY SHOULDN T YOU LIFT FROM A BENT POSITION? Your goal is to explain why this exercise is not good for the back muscles (represented by the cable) and even worse for the 1---inch diameter fluid filled discs in the lower back (represented by the joint). Provide a complete analysis, including: a) A sketch, force diagram, and list of assumptions b) Equations representing the conditions of equilibrium, specialized to this situation c) A calculation of the muscle tension (the tension force exerted by the cable on the beam) and compression of the back at the joint (the contact force exerted by the joint on the beam). Note: Because the horizontal beam is connected to the wall by a joint, the normal force exerted by the wall on the horizontal beam does not have to be perpendicular to the wall.
11 APPLICATION EXPERIMENT: BICEPS DESIGN Your task is to design and build an apparatus that replicates the lower arm and biceps muscle system. Available equipment: Section of meter stick, ring stand, 2 clamps, hangers, objects to hang, spring scale The human arm can be modeled as follows. The object of interest should be the bones in the lower arm (forearm) and hand (together modeled as a rigid beam). It interacts with an object held in your hand, with the biceps muscle, with the bone in the upper arm at its joint with the forearm, and with the Earth. Use the following steps to build the apparatus for the arm: a) Draw a labeled sketch of your proposed apparatus. Hint: Brace the system at the elbow so the elbow can t move but the forearm can rotate around it.
12 b) Construct a force diagram for the forearm. You will have to decide what forces to include, and where they are applied by carefully considering the other objects interacting with the beam. Hint: Hold a heavy object in your hand, with your forearm parallel to the floor. Feel different parts of your arm to decide what objects interact with your forearm, and where those objects exert forces on your forearm. Remember, the system is your forearm and hand only, everything else is part of the environment and could exert forces on your forearm. c) List the equipment you will use to model the beam, the bicep muscle, and the elbow joint. d) Mathematically determine the force exerted by the bicep muscle on the forearm while the artificial arm is holding an object in its hand. To do this, develop a mathematical procedure that involves the conditions of equilibrium. e) What assumptions did you make in your mathematical method? How could they affect the result? f) Build the apparatus, and note the reading on the biceps spring scale. g) Compare the force you determined mathematically with the outcome of the experiment. Lastly, how does the force exerted by the bicep on the forearm compare with the force exerted by held object on the forearm? What does this reveal about the efficiency of the human arm, and what is the reason for it?
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