Addition of Force Vectors for Bodies in Equilibrium

Lab Partners’ Names: ______Period______

APC Physics Lab: Newton’s First Law for Vector Addition Applied to Bodies in Equilibrium

Purpose: To demonstrate Newton’s First Law of Motion for a stationary body through the use of vector addition both graphically and by component.

Testable Question: Will the vector sum of forces acting on a motionless body (a body in equilibrium) add up to ZERO both by graphical and component addition?

Research: Text book or other sources: o Newton’s First Law of Motion as it pertains to motionless bodies o Vector addition and Resultants

Discussion: ( expectations) : By adding together the vector forces acting on a stationary body, a resultant force of zero (no resultant) should be obtained.

Procedure: o Set up equipment as shown below. o Obtain the data sheet (each student has their own data sheet) and: o Tape data sheet to table so as not to move o Trace force wheel on paper o Mark a dot on paper where center of force wheel is o Hang weights (no less than 200 grams on any cord) off table over pulleys so that wheel stays stationary o Trace the three string directions when wheel comes to rest o With one string set a 0 degrees, measure and record angles between strings on data table and on data sheet. o Record gram-force acting on each string on both the data table and on data sheet. o Decide on and record the scale you are using for the gram-force vectors o Convert the line tracings into scaled vectors o Add the scaled vectors together head-to-tail using a protractor and ruler, making sure not to change their direction or scaled length when moving and adding them. o Draw and label the resultant of your vector addition o Measure your resultant length and convert to the gram-force it represents, recording this force on your data sheet and in your data table. o Calculate the x- and y- components of the two vectors that are not at 0o and record their values along with the vector at zero degrees in the table. o Add the x- and y- components together. o Use the x- and y-components to find a resultant value. o Compare this resultant to the graphically-found resultant using a percent Difference calculation. o ATTACH your original data sheet to your lab so that it folds out easily for measurement by me Stationary knot Force Wheel

Mass 1

Mass 3

Mass 2 Materials: o Paper, force wheel, protractor, metric ruler, string, three 500 gram spring scales, tape, various weights (no less than 200 g on any string)

Data: Scale used to represent vectors: 1 cm = ______grams

Length of Graphical Addition Resultant vector: ______cm = ______grams

Vector Gram- Length of Calculated Calculated Calculated Angles force Vector x- y- Resultant used (cm) component component (cm) (g) (cm) (cm) 0o

Total of x- and y- components

Sample Calculations:

Quantity Formula Substitution Answer Units Vector gram force conversion to length Resultant Length Conversion to gram force Calculated x-component Calculated y-component Calculated Resultant Conclusion Questions: 1. What does it mean if you got a resultant vector measurement greater than zero?

2. How close were your graphical and vector component addition resultants? Indicate this with a calculation of % Difference: (SHOW the calculation and comment on it…)

% Difference = |One value – Average of Values| (100) Average of Values

3. What can you briefly say about the merit/detriments of each method of vector addition? Vector Merits Detriments Addition Style Graphical Method

Sum of Component Method