Lab 4: Forces and Vectors

Equipment: Force Table and Accessories, 50 Gr. Hanger, Assorted masses The goal of this lab is to put a system into equilibrium by predicting a balancing force using both a graphical and component methods. Use only graph or the protractor paper to plot the vectors. Part I Predictions: Balancing 3 Forces • Using the graphical method (also called tip-to-tail method), find the resultant vector R =

A + B where A=(600.0 grams, 30.0º) and B= (400.0 grams, 130.0º). Use a scale of 1 mm = 10 grams.

• Using a ruler and a protractor, accurately draw R = A + B and then measure the magnitude and angle of R. How many significant figures are you keeping and why?

• Use the component method to calculate the balancing force and compare your results with the graphical method. Your graphical method and component method should agree within a few percent. Include these calculations in your lab report.

• Record your results in your lab report: Scaled Values for A and B (mm) Predicted Values of R from graphical method Predicted Values from component method Percent Difference Between methods Print out a copy of the protractor paper (the last page of these instructions) and plot your three vectors: A, B, and R. This will serve as a map for Part III.

Part II Predictions: Balancing 4 Forces • Now repeat the above process for predicting the balancing fourth force with the

graphical method when three forces are given: A=(250.0 grams, 30.0º), B= (475.0 grams, 110.0º) and C=(325.0 grams, 300.0º). Use tip-to-tail vector addition.

• Use the component method to find the balancing force and compare your results with the graphical method. Your graphical method and component method should agree within a percent or two. If they don’t, redo the graphical method more carefully. Include your calculation in your lab.

• Record your results in your lab report: Scaled Values for A, B, and C (mm) Predicted Values of R from graphical method Predicted Values of R from component method Percent Difference between methods

Print out a second copy of the protractor paper and plot your four vectors: A, B, C, and R. This will serve as a map for Part III. Part III: The Experimental Test • After you have finished your predictions, show your work to the instructor who will give

you a force table if you are ready to do the test! • On the force table, place pulleys at the positions of vectors. • Pass the strings attached to the central ring through pulleys and hang the appropriate

amount of mass from it. Don’t forget that the hanger itself has a mass of roughly 50 grams.

• If your predictions are correct, all the forces should be balanced and the center pin should be located in the center of the ring.

• If the forces don’t balance, try to find the location and mass of balancing force by trial and error.

• If the forces balance, try perturbing the system by pushing the ring very slightly to one side. Does it (eventually) return to equilibrium?

• Repeat for the 4 forces. • Explain your results in a brief summary.