WeightliftingPROBLEMPROBLEM SKILLSBaCKGROUND INFORMATIONproblem solvingOBSERVATIONSIntroductory MechanicsProblems Laboratory1WeightliftingGoals: 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.2 WeightliftingPROBLEM 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 INFORMATIONIn 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.Wmg=Weightlifting 3(EQ 2)An important property is the projection of a vector onto a one of the coordinate axes. We will use two axes, the x-axis for the horizontal direction, and the y-axis for the vertical direction. If a vector of magnitude A is projected onto an axis at an angle θ to the vector, the magnitude of the projection is P, where(EQ 3)This type of projection gives the components of a vector. A 2-dimensional vector has components in the x and y directions, for instance Ax and Ay. Components do not have arrows because they are not vectors, they are the components of vectors.Any time an object is at rest or moving at constant velocity, the Newton’s first law, the law of inertia, can be used. For an object acted on by more than one force, the sum of the force vectors must be zero. This is true in each separate coordinate. If one of the forces in a coordinate is unknown, and the object is at rest or constant velocity, the unknown force can be found by adding up all of the forces in that direction and setting them equal to zero.PROBLEM SOLVING Part A. Setting up the Problem1. Have each person in your group make an individual guess for the force needed in each arm without using math.2. Share those answers with your group and discuss who might be closest.3. Based on the picture, draw a force diagram for the forces acting on the barbell and weights when held over the lifter’s head.4. Assign variables to each of the forces in the diagram.5. Use EQ 1 to find the weight of the barbell.6. Estimate the angles of each of the arms acting on the bar.7. Use EQ 3 to write expressions for the components for each of the force vectors.8. Write equations for each of the two coordinates using your expressions from step 7.9. Solve the equations in step 8 to find the force in each arm.10. Share your methods and results (the diagrams and mathematical expressions) with the other groups.Part B. Comparing to Similar Situations11. Make a force diagram for a barbell held at waist level just before the lift.12. Repeat steps 4 through 9 for the diagram in step 11.13. Make a force diagram for a barbell as it is lifted past the eyes.14. Assume that the barbell is moving with constant velocity and repeat steps 4 through 9 for the diagram in step 13.15. Share your results with the other groups.CAB+=PAθcos=4 WeightliftingOBSERVATIONS How much variation was there in the answers shared in step 2? What concepts were