vector addition of forces

Purpose:

To study vector addition by:

1) Graphical means and by

2) Using components.

A circular force table is used to check results.

Equipment:

Circular force table, masses, mass holders, string, protractor, four pulleys.

circular force table / four pulleys

protractor

Procedure:

1. Your instructor will give each group three masses in grams (which will

represent the magnitude of three forces) and three angles. Choose a scale of

1 cm = 20 grams, make a vector diagram showing these forces, and

graphically find their resultant. Determine the magnitude (length) and

direction (angle) of the resultant force using a ruler and protractor.

2. Make a second vector diagram and show the same three forces again. Find

the resultant vector again, this time by components. Show the components of

each vector as well as the resultant vector on your diagram. Draw the force

(vector) you would need to exactly cancel out this resultant.

3. Mount three pulleys on the edge of your force table at the angles given

above. Attach strings to the center ring so that they each run over the pulley

and attach to a mass holder as shown in the figure below. Hang the

appropriate masses (numerically equal to the forces in grams) on each string.

Is the ring in equilibrium? Set up a fourth pulley and mass holder at 180

degrees opposite from the angle you calculated for the resultant of the first

three vectors. Record all mass and angles. If you now place a mass on this

fourth holder equal to the magnitude of the resultant, what happens? Ask

your instructor to check your results before going on.

figure 1

figure 3

figure 2

figure 4

Vector Calculations:
Rx = (100Cos(0)) + (200Cos(71)) + (160Cos(144)) = 36.1
Ry = (100Sin(0))  + (200Sin(71))  + (160Sin(144))  = 283
ø = 82.7°              R = sqrt(283^2 + 36.1^2) = 285.3  



The simulation confirmed the results as correct. *Note: scale to 1=10.

The diagram shows vectors A, B, C and D as the sum. (1 cm = 20 g)

figure 8

conclusion:during our lab experiment we learned that in order to get three forces that where given. to be in equilibrium a forth force would be necessary to counter- balance the other three forces this force would have to be negative and would be the sum of all 3 forces.

lab2

purpose:

1To determine the acceleration of gravity for a freely falling object         

2 To gain experience using the computer as a data collector.

equipment:



 

logger pro

motion detector

•  wire basket
• rubber ball

Introduction:

         In this lab we use the computer to collect some position(x)vs. time (t)data for a rubber ball being tossed in to the air > since the velocity of an object is equal to the slope of the x vs. t curve, the computer can also construct the graph of v vs. t by calculating the slope of x vs. t at each point in time.We  will use the both the x vs. t graph and the v vs. t graph to find the free fall acceleration of the ball.

procedures:1.  Connect the lab pro to computer and motion detector to DIG/SONIC2 port on lab pro. Turn on the

computer and load the Logger Pro software by double clicking on its icon located within the Physics

Apps folder. A file named graph lab will be used to set up the computer for collecting the data

needed for this experiment.  To open this file, first select File/Open and then open the mechanics

folder. When this folder opens, open the graph lab file.

2.  You should see a blank position vs. time graph.  The vertical scale (position axis) should be

from 0 to 4 m while the horizontal scale (time axis) should be from 0 to 4 s.  These values can be

changed if you desire by pointing the mouse at the upper and lower limits on either scale and

clicking on the number to be changed.  Enter in the desired numbers and push the Enter key.

3.  Place the motion detector on the floor facing upward and place the wire basket (inverted) over

the detector for protection from the falling ball.  Check to see that the motion detector is

working properly by holding the rubber ball about 1 m above the detector.  Have your lab partner

click on Collect button to begin taking data and then move your hand up and down a few times and

verify that the graph of the motion is consistent with the actual motion of your hand.  After 4s

the computer will stop taking data and will be ready for another trial.  If your equipment does not

seem to be working properly ask for help.

4.  Give the ball a gentle toss straight up from a point about 1 meter above the detector.  The

ball should rise 1 or 2 m above where your hand released the ball.  Ideally your toss should result

in the ball going straight up and down directly above the detector.  It will take a few tries to

perfect your toss.  Be aware of what your hands are doing after the toss as they may interfere with

the path of the ultrasonic waves as they travel from the detector to the ball and back.  Take your

time and practice until you can get a position-time graph that has a nice parabolic shape.  Why

should it be a parabola?

5. Select the data in the interval that corresponds to the ball in free fall by clicking and

dragging the mouse across the parabolic portion of the graph.  Release the mouse button at the end

of this data range.  Any later data analysis done by the program will use only the data from this

range.  Choose Analyze/Curve Fit from the menu at the top of the window.  Choose a t^2+ b t + c

(Quadratic) and let the computer

find the values of a, b, and c that best fit the data.  If the fitted curve matches the data curve,

select Try Fit.  Click on OK if the fit looks good.  A box should appear on the graph that contains

the values of a, b, and c.  Give a physical interpretation and the proper units for each of these

quantities (Hint: use unit analysis).  Find the acceleration, gexp, of the ball from this data and

calculate the percent difference

between this value and the accepted value, gacc, (9.80 m/s2).

6. Look at a graph of velocity vs time for this motion by double clicking on the y-axis label and

select “velocity” and deselect “position”.  Examine this graph carefully.  Explain (relate them to

the actual motion of the ball) the regions where the velocity is negative, positive, and where it

reaches zero.  Why does the curve have a negative slope?  What does the slope of this graph

represent?  Determine the slope from a linear curve fit to the data.  Find the values of m and b

that best fit the data. Give a physical interpretation and the proper units for each of these

quantities (Hint: use unit analysis). Find the acceleration of the ball, gexp, from this data and

calculate the percent difference between this value and the accepted value, gacc. Put together an

excel spreadsheet for your data like the one shown below. Finally, select Experiment/Store Latest

Run to prepare for the next trial.

7.  Repeat steps 4 - 6 for at least five more trials.  Obtain an average value for the acceleration

of gravity and a percent difference between this value and the accepted value.

  

Results:


table

  

trial 1



trial 2



trial 3



trial 4

trial 5

conclusion: This lab gave us a clear understanding of object being thrown in the air gave us more practice on using the software logger pro and using motion detector to detect the data of our ball when we through it up in the air. from our results we where able to find the slope for each trial.most of our trials where near our gravitation force our percent error was about -1.2% difference.