Exercise on Vectors using the Simulation on PHET: https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html Part 1: decomposition of a Vector into its rectangular components....

Exercise on Vectors using the Simulation on PHET: https:
phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html
Part 1: decomposition of a Vector into its rectangular components.
Given a vector A: magnitude = 60 units pointing at a angle of 40 degrees to the x axis.
Create a triangle by dropping a line from the tip of the vector to the x axis. Use your knowledge of geometry to find the sides of the triangle which are the x and y components of the vector.
In this exercise, you will start with a vector and calculate its x and y components on a sheet of paper. Ax = A Cos q and Ay = A Sin q XXXXXXXXXXAx = _____________ Ay = __________
If you have graph paper, draw the vector to scale 10 units = 1 cm and measure the length of the three sides of the triangle. Is the length of the sides co
ect? Ax should be 10 times the Length of x. what about Ay ?
Now open up the simulation click on “explore 2 D” at bottom of screen. Drag vector a from right and position the bottom of the vector at the origin. Now drag the tip to a length of 6 units and rotate the vector to an angle of 40 degrees. See the values at the top of screen. Notice the values of Ax and Ay . do they agree with your values? You can click on the triangle description available on the right.
Part 2
Vector Addition.
A = 6 units angle 20 degrees, B = 8 units angle = 140 degrees.
Calculate the x and y components of both A and B.
Ax = ___________     Ay = ____________
BX = ___________        By = _____________
Ax + Bx = _____________ Ay + By = ___________
Set up the simulation , drag vector A so that it starts at the origin and has 6 units and 20 degrees; then drag vector “b” from box on lower right so that the end is at the a
ow head of vector A. Drag the a
ow head of vector b so that it is 8 units and 140 degrees from the x direction. Now click on the sum on the upper right, the sum vector appears in the work area. Drag the sum vector so that the tail is at the origin; notice that the head is at the head of vector b.
Now add the following vectors, A = 6 units angle 30o B = 10 units angle 120o C = 8 units angle 250o XXXXXXXXXXSolve analytically, (by components) then set up the simulation and solve it using the simulation. Compare, did it work?

NEWTON'S SECOND Law
Introduction: Newton's Second Law is a statement of the cause and effect relationship between the force and the acceleration. The force produces the acceleration. Newton's Law says that the acceleration of an object is directly proportional to the force pulling the object (the mass remaining the same). It also says that if the force is kept constant, the acceleration is inversely proportional to the mass of the object. This is summed up in the mathematical statement: Fnet = M a Where F is the net force acting on the object and M is to total mass of the objects being accelerated.
In Atwood’s Pulley experiment, the net force is due to the difference in the weights since one weight wants to rotate the pulley to the right and the other weight wants to rotate it to the left. If the weights were equal the forces would cancel each other out and there would be no acceleration. So the net force = m1 g – m2 g , and the total mass of the system is m1 + m2. Since the net force is small the acceleration should be small enough to measure by timing the falling weight to fall a distance y from a stationary position (zero velocity). a = 2* y/ t2.
Then the net force can be increased without increasing the total mass by transfe
ing mass from m2 to m1, so m1g – m2g increases.
In verifying that the acceleration is inversely proportional to the total mass of the system, the net force must remain the same. So start with m1 greater than m2 and add equal amounts of mass to both m1 and m2, so that the total mass increases but the difference remains the same.
To construct the apparatus, I looked around for a pulley (I’m going to use spools for thread. For weights I use a box of nuts (like for screws) and a paper clip for a hook to hold the nuts. I will use a light string.
Diagram of apparatus: (make your own) use a ruler, and a pencil.
Part I: the dependence of acceleration on the net force
It would be nice to know how much the nuts weigh, if you have a kitchen scale you can weigh them and use the mass of the nuts.
accel(th)= (m1 – m2) g/(m1 + m XXXXXXXXXXacc(meas) = 2 y/t2
    M1 (nuts)
    M2 (nuts)
    (m1 + m2)
    (M1-m2)g
    time
    Acc(th)
    Acc (meas)
    % e
o
    8
    6
    14
    2*9.8
    0.84
    1.4
    1.4
    0
    9
    5
    14
    4*9.8
    0.59
    2.8
    2.9
    3.4
    10
    4
    14
    6*9.8
    0.49
    4.2
    4.16
    1.0
    11
    3
    14
    8*9.8
    0.42
    5.6
    5.67
    0.5
Table I: y = 50 cm


Now plot a graph of acceleration (y axis) and the net force (m1-m2) g on the x-axis. Note if you do not know the mass of a bolt use the number of bolts. (the units of mass will cancel). As an experimental design problem, it would be better if you have many washers instead of nuts, then the net force would be smaller and the acceleration smaller and the time longer (easier to measure). M1 = 18 washers and m2 = 16 washers and increase the y to 90 cm (0.9 meters). The numbers in the tables are fictional.
For the graph make two columns x,y in excel
    F net
    Acc (meas)
    19.6
    1.4
    39.2
    2.9
    58.8
    4.7
    78.4
    5.67
Legend: what does this graph indicate? What is the meaning of the slope?
(go to the equation and rea
ange the terms.
A = {1/(m1 + m2)}* Fnet The slope should be equal to the value of {1/(m1 + m2)}
Now you need to do part II. The dependence of the acceleration on the mass of the system which is (m1 + m2).
Keep the difference constant and increase both by the same amount. See the table II.

    M1 (nuts)
    M2 (nuts)
    (m1 + m2)
    (M1-m2)g
    time
    Acc(th)
    Acc (meas)
    % e
o
    4
    2
    6
    2*9.8
    0.55
    3.27
    3.31
    1.2
    6
    4
    10
    2*9.8
    0.71
    1.96
    1.98
    0.4
    8
    6
    14
    2*9.8
    0.84
    1.4
    1.42
    1.0
    10
    8
    18
    2*9.8
    0.96
    1.09
    1.09
    0.0
Now make a graph of acceleration (meas) y-axis and total mass (x-axis)
Finally make a statement to
ing part I and part II together. This summary statement should include the two premises (a proportional to Fnet) and (accel inversely proportional to total mass).
¤    
*Determine the% difference. Did the acceleration increase with increased force?
Part II (keep the hook weight at maximum and change the mass of glider)
*Place all sloctted weights on the hook weight.(21 grams)
*Add the 50 gram weights (silvery with the hole in the center) to each side of the glider (total additional mass = 100 gm) and repeat the acceleration measurement.
*Repeat this procedure, incrementing the mass of the glider by 100 grams.
*Compare the acceleration measured with the theoretical value: a =
!ö    …
!
¤    
*Determine the% difference. Did the acceleration decrease with increased total mass?
Data Sheet    Name _______________________________ Date ____________ XXXXXXXXXXGroup # ____
Lab Partners _______________,___________________
Make your own table in your notebook.
                    ABCDEFG1Mass (M1)ForceGlider (M2)Total MassAccelerationM1g/(M1+M2)%E
or2 (kg)(N)(kg)(Kg)from graph(m/s^2)     XXXXXXXXXX    
                                    Mass (M1)ForceGlider (M2)Total MassAccelerationM1g/(M1+M2)%E
or (Kg)(N)(Kg)(Kg)from graph(m/s^2)    
                    
Problems:
1) Two students measured the time it takes for the 200 gm. glider to travel 50 cm from rest. Their data for ] T was as follows: XXXXXXXXXXsec., 0.716 sec., 0.714 sec. What was the mass of the decending weight, M1? (Ans. M1 = 50 grams)
2) In verifying Fnet = M a , the net force was kept constant for several readings while the total mass was increased. Graph acceleration on the "y axis" and "1/…MM¤" on the "x axis". In order to plot this graph you will need a new column in your table for 1/…MM¤. Is your graph a straight line? What is the slope of the graph? What should your slope be equal to?
3) Make a graph to show that the acceleration varies directly with the net force (Mg) when the mass (M+ M) was kept approximately constant. (Note the force caused the change in the acceleration so the force goes on the "x axis".) Find the slope...Is it equal to 1/…MM¤?
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@~°
4°    4°    ”ÿÿÿ
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acceleration vs. net force
XXXXXXXXXX     XXXXXXXXXX    58.8     XXXXXXXXXX    1.4    2.9    4.7    5.67    net force
Axis accelerationTitle

Galileo’s Motion lab:1
Galileo’s described acceleration as:
A motion is said to be uniformly accelerated, when starting from rest, it acquires, during equal time-intervals, equal increments of speed. (discourse on two new sciences day 3) This implies that when an object falls it increases its speed so that its speed in the 2nd second is twice that as its speed in the first second and its speed in the 3rd second is three times its speed in the first second and