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VECTOR ADDITION
Purpose The purpose of this experiment is to use the force table to experimentally determine the force B which balances two other forces F1 and F2. This experimental result will be compared with the theoretical evaluation of B.
Procedure
Hang the following masses on two of the pulleys and clamp the pulleys at the given angles: SET 1: Force F1 = 50 gr at 270° Force F2 = 100 gr at 30° By trial and error, find the angle for the third pulley and the mass which must be suspended from it that will balance the forces exerted on the strings by the other two masses. The third force is called the balancing force B since it is the force which establishes equilibrium. B is the negative of the resultant F1 and F2.Ring Method of Finding Equilibrium To determine whether the system is in equilibrium, use the following criteria. The ring should be centered over the post when the system is in equilibrium. Screw the center post down so that it is flush with the top surface of the force table and no longer able to hold the ring in position. Pull the ring slightly to one side and let it go. Check to see that the ring returns to the center. If not, adjust the mass and/or angle of the pulley until the ring always returns to the center when pulled slightly to one side. Record the mass and angle required for the third pulley to put the ring into equilibrium. B-experimental = 85 gr = experimental magnitude of B "force" Angle-experimental = 178o ------------------------------------------------------------------------------------------ ANALYSIS OF SET 1 Step 1: Force F1 = 50 gr at 270° => F1 = (0, -50) Force F2 = 100 gr at 30° => F2 = (100 cos30, 100 sin30) = (86.6, 50) R = F1 + F2 => R = (86.6, 0) |R| = R = √(86.62 + 02) = 86.6 = 87 gr
B is the negative of the resultant F1 and F2. So, B = - R => B = (-86.6, 0) |B| = B = √[(-86.62) + 02] = 86.6 = 87 gr = theoretical magnitude of B To find the direction of B draw it in a coordinate system:
Based on the above drawing B is directed at 180o counterclockwise from the positive x-axis.
Step 2: Draw to scale on the circular graphing paper, forces F1, F2 and the theoretical B. If =: means "corresponds" then assume: length of F1 =: 3 cm =: 50 gr at 270° length of F2 =: 6 cm =: 100 gr at 30° To find the length of B do:
hence length of B =: 5 cm at 180°
Step 3: Find experimentally the mass (that is, B-experimental) and angle (Angle-experimental) required for the third pulley to put the ring into equilibrium. Record them as: B-experimental = 85 gr Angle-experimental = 178o
Step 4: Find % differences between the theoretical values of the magnitude and direction of the balancing force B-theoretical and the experimental values of the magnitude and direction of the balancing force B-experimental. In other words compare:|B-theoretical| = 87 gr with |B-experimental| = 85 gr
Angle-theoretical = 180o with Angle-experimental = 178o
Repeat procedure and analysis for the following two sets as well as a set of your own.
ANALYSIS OF SET 2 Step 1: Force F1 = 50 gr at 20° => F1 = ( ... , ... ) Force F2 = 100 gr at 70° => F2 = ( ... , ... ) R = F1 + F2 => R = ( ... , ... ) B = - R => B = ( ... , ... ) Prove B = (-81.2, -111.1) |B| = B = √[(-81.22) + (-111.1)2] = 138 gr = B-theoretical Draw B in a coordinate system to find: Angle-theoretical = 234o counterclockwise from the positive x-axis
Step 2: Draw to scale on the circular graphing paper, forces F1, F2 and the theoretical B.
Step 3: Find experimentally the mass (that is, B-experimental) and angle (Angle-experimental) required for the third pulley to put the ring into equilibrium. Record them as: B-experimental = ... Angle-experimental = ...
Step 4: Find % differences between experimental and theoretical results.
ANALYSIS OF SET 3 Step 1: Force F1 = 100 gr at 30° => F1 = ( ... , ... ) Force F2 = 100 gr at 150° => F2 = ( ... , ... ) R = F1 + F2 => R = ( ... , ... ) B = - R => B = ( ... , ... ) Prove B = (0, -100) |B| = B = √[(02) + (-100)2] = 100 gr = B-theoretical Draw B in a coordinate system to find: Angle-theoretical = 270o counterclockwise from the positive x-axis
Step 2: Draw to scale on the circular graphing paper, forces F1, F2 and the theoretical B.
Step 3: Find experimentally the mass (that is, B-experimental) and angle (Angle-experimental) required for the third pulley to put the ring into equilibrium. Record them as: B-experimental = ... Angle-experimental = ...
Step 4: Find % differences between experimental and theoretical results.
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