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Introductory Mechanics Problems Laboratory
Weightlifting
Goals: Make estimates from real situations. Use vectors graphically and numerically.
PROBLEM Weightlifting is an old sport that tests the pure strength of competitors. It also has attracted research from physics. There are many physical considerations relating to the grip and the method to lift. Lifters of different weights can compete, and Dr. David Meltzer of Iowa State has studied these relationships. He also competes at an interna- tional level of competition as in the picture below from 1999 in Glasgow, Scotland where he lifted 135 kg (298 lbs).
As scientists your task is to estimate the force in each arm used to hold the weight up and compare it to the force needed in the arms to make the lift.
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PROBLEM SKILLS The question posed above requires a number of steps to reach an answer. How do we separate steps? Usually there is a formula that we think applies to the problem. That for- mula will have some number of variables. One step may be drawing a diagram to help identify those variables. Once you have a formula you should identify which variables are already known and which are unknown.
Many problems include numerical values. In general, when we set up problems we should assign variables to each numerical value in the problem. There are a number of good reasons to do this. It is easier to see the form of the equation when physical quanti- ties are left as variables. If there are terms that exactly cancel, variables make that clear. It is usually easier to misplace a number than a variable, so solving equations with vari- ables is less prone to error. In the end the numeric values can be inserted in place of the variables to get a numeric result.
If there is more than one unknown variable in the formula, you will need to add steps to reduce the number of unknowns to one. This means finding a value for all the unknown variables except one. Sometimes an unknown variable can be filled by an estimate using rounding or order of magnitude approximations. Other times another formula will be needed to get that value.
When all but one of the variables in a step are known, the steps can be completed. You may have to rearrange the formula to solve for the remaining unknown variable. After finding the unknown value, you should check the precision of the result. You should use the same number of significant figures as for the least accurate value that goes into the formula.
BACKGROUND INFORMATION
In mechanics many problems are based on the forces acting on an object. A force is a push or a pull acting on that object from outside the object. Forces are vectors with mag- nitudes and dircetions. Some comon forces are due to tension, compression, and weight. Tension is a force due to someing pulling on the object and compression is a force where the object is pushed. Weight W is the force on an object due to gravity acting on its mass m and can be expressed as
(EQ 1)
where g = 9.81 N/kg.
One of the most important tools to work on force problems is the force diagram. In a force diagram, you draw a vector indicating the force for each separate force acting on the object in question. Try to avoid mixing forces acting on different objects in the same diagram - use more diagrams if necessary. After marking the forces on the diagram pick a coordinate system for your diagram and find all the components of the forces using your chosen coordinate system.
Graphically we designate vectors by arrows, and an arrow over a variable means that it is a vector. The tail of the arrow shows the origin of the vector, and the tip indicates the direction of the vector. The length of the vector is proportional to the magnitude. Vec- tors can be added graphically by placing the moving the tail of a second vector to the head of the first vector keeping the magnitude and direction the same. The vector sum is a vector that point from the tail of the first to the head of the second vector.
W = mg
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OBSERVATIONS How much variation was there in the answers shared in step 2? What concepts were people relying on to make their guesses?
What information did you assume to estimate the angles in step 6 and how accurate were those estimates?
There should have been two equations in step 8. Did you need to solve both to find the force in step 9? Why or why not?
Compare the results from all the groups in step 10. How much variation was there, and what was the likely cause?
What caused the forces to be the same or different in magnitude in step 12 and 14 com- pared to step 9?
Are the magnitude of the forces in the arms the likely factor in our sense of the difficulty when holding the barbell in any of the three positions?
