Vector Addition: Experimental Verification using Graphical and Component Methods, Lab Reports of Art

Download Vector Addition: Experimental Verification using Graphical and Component Methods and more Lab Reports Art in PDF only on Docsity! VECTOR ADDITION PURPOSE: To experimentally verify the rules for vector addition by graphical (scale drawing) and by components. APPARATUS: Force Table with Pulleys 50g mass holders Assortment of masses from 1g to 100g METHOD: Forces produced by masses attached to strings over pulleys are vectors used in this experiment. The directions of the vectors can be varied by positioning the pulleys at different points around the rim of the circular force table. The magnitudes of the vectors are changed by varying the masses on the strings. At the center of the force table, all of the strings are attached to a plastic ring. (See Figure 1). F a FF F b R E Figure 1 You are given two (or three) forces, which are called Fa and Fb (or Fa, Fb and Fc), and your problem is to find their resultant FR. FR is the result of the combined actions of Fa and Fb (or Fa, Fb and Fc). What you actually find on the force table is the equilibrant, FE of the given forces: the force that balances them, so there is no tendency for the central ring to start moving when FE is applied along with the given forces. The resultant, FR has the same magnitude as FE, and its direction is opposite to that of FE. The direction of FR is found by subtracting 180° from the angle found for FE. PROCEDURE: 1. Given forces are Fa = 500 at 0° and Fb = 500 at 120°. 2. Place pulleys at the positions of the given forces and add the necessary masses to produce Fa and Fb (include the mass of the holder). Remove any unused mass holders from their strings. 3. Find the angle for FE by positioning another pulley roughly opposite the given forces and pulling the string with your hand over the pulley. If you cannot center the plastic ring on the central pin by pulling the string down over the pulley, the correct angle has not been found. Move the pulley for FE in steps of about 5° along the rim toward the direction where the ring touches the central pin, until you find the position where the ring can be centered by pulling the string over the pulley. It might be necessary to slide the strings slightly where they are tied to the ring to make the line of the string pass through the center of the pin. You may also need to use finer angular adjustments as you approach the proper position. 4. Put a mass holder on the string you have been pulling and add masses until the plastic ring is centered, with no tendency to move when you tap the force table with your hand. 1 5. Record all of the angles and masses with their uncertainties in accord with your teacher's instructions. 6. Repeat steps 2 through 5 for Fa = 300 at 30° and Fb = 400 at 80°. 7. Repeat steps 2 through 5 for Fa = 200 at 0°, Fb = 100 at 70° and Fc = 100 at 160°. 8. Find the approximate error due to friction by putting 500g on one string and 500g on a second string directly opposite. Find how much mass must be added to one side for the ring to move noticeably (a) When the mass is added gently. (b) When the table is tapped as they are added. ANALYSIS: 1. Find the experimental value of FR for each of the three different setups. Remember that the magnitude of FR is the same as that for FE and that the angle for FR is that of FE minus 180°. Show any calculations and record these values on your calculations page. 2. Find FR for each setup using the graphical method (scale drawing). Choose a reasonable and convenient length scale to represent the vector magnitudes, then using a protractor and ruler lay out the given vectors head to tail. FR runs from the tail of the first to the head of the last vector. Use a scale sufficiently large that the completed drawing nearly fills half of an 8 1 2 ×11 page. Label all magnitudes and angles on the drawing and list the scale used. 3. Find FR by the method of components (using trigonometry) and show your work on the calculations page. See your text if you don't remember how to do this. 4. Find the percent difference comparing the magnitudes only of the experimental results to the component method results and also comparing the magnitudes of the graphical results to the component method results. 5. Calculate the percent error expected due to friction from your data in step 8-b. Your results table should look something like this: |< Include angles >| Setup FR Exp. FR Graph. FR Comp. % Diff. Experimental % Diff. Graphical Friction % error 1 2 3 Vector Addition 2