Download Day 1 Notes: Dealing with projectiles in two dimensions. There are

Day 1
Notes:
Dealing with projectiles in two dimensions.
There are no forces acting on horizontal projectile. No acceleration.
Ertical: negative 9.8
Projectile: an object that is acted upon only by gravity. It must be moving in two dimensions.
LAB: Ball and ramp lab
Hypothesis: The horizontal distance of a projectile can be calculated by the x and y chart and kinematics
even when the vertical initial velocity is not provided.
Data table:
Calculations:
Analysis:
We set the vertical initial velocity to zero and we were able to calculate the horizontal distance
by using the x and y chart and kinematic formula. However, there was 10% error from the photogate
timer measurement. The result from the photogate timer was more accurate than the calculations. I
think that there is a possibility of the vertical initial velocity not being zero.
HOMEWORK:
1. What did you that you already understood from our class discussions?
-
I already understood the concept of projectile. A projectile is an object that continues in
motion when it is projected. Gravity is the only force acting downward. Without the gravity,
because gravity only influences vertically, a projectile will undergo a non stop horizontal
motion.
-
I also understood that the projectile is in both vertical and horizontal ways and they are
independent of each other. Horizontal movement is motion without acceleration. However,
vertical motion is constantly acted upon by the force of gravity pulling the object down.
Thus, increasing the speed of the projected object.
-
Horizontal displacement of a projected object can be found by the formula: x=V initial * T. I
understand the calculations and the math of this lesson.
2. What did you read that was little confusing?
-
No concept was specifically confusing. However, I did not understand the fact that a
projectile could continue moving without the force of gravity working downwards at first. I
totally understand the fact now. Also, I had some trouble with finding hang time and range
using the x and y chart. However, with the instructor’s(teacher’s) help, I do not have any
problem with the math now.
3. What did you read that you still do not understand?
-
I basically understand every concept now.
4. What did you read that was not gone over during class today?
-
Day 2:
We went over everything in the class. Frankly, I do not remember; there might be
something that we did not go over but I think those things are too basic or trifling to go over
during the class time.
LAB:
Objective: what is the relationship between the angle of incline nad the acceleration.
Hypothesis: the greater the angle of incline, the faster the speed of an object.
Data table:
H
Angle
T1
T2
T3
Average Time
Distance
Acceleration
Track
0.043
2.02
2.15
2.25
2.18
2.19
1.03
0.428
1.22
0.081
3.81
1.53
1.63
1.56
1.57
1.03
0.832
1.22
0.069
3.24
1.75
1.88
1.88
1.83
1.03
0.611
1.22
0.196
9.24
0.9
1.03
0.97
0.967
1.03
2.205
1.22
0.282
13.36
0.75
0.75
0.72
0.74
1.03
3.762
1.22
Graph:
Analysis:
The relationship between the angle of incline and the acceleration is proportional. The greater the angle
of the incline, the faster the cart went dwon the track. The smallest angle was 2.03 degrees and the
acceleration was 0.428 m/s/s. The biggest angle was 13.36 degrees and the acceleration for that angle
was 3.76 m/s/s. In theory, the formula for the slope was g=sin theta, making the slope 9.8. However,
the experimental result comes out to be 16.91. The percent error was 75.2%. This error comes from the
reaction time between the student who let the cart go and the student who pressed the stop watch.
This error could be minimized by using a photogate timer. Also, the error would be minimized if the
same person did both works.
Notes:
Newton’s gravity law, Law of universal gravitation.
Gravitation of force is directly proportional to the product of the mass
of the two objects. Newton deduced that it is inversely proportional to the square of the distance.
Distance is always measured center to center.
G is universal gravitation constant.
G=6.67 % 10 to the negative 11t
hCappler’s
planet laws
planetsmove in elliptical orbits around sun with sun at one focus.
Any given amount of time the planet will carve out equal areas in its orbit around the sun: law of equal
areas
The closer to the sun the faster you are moving.
Period square divided by the distance by the sun cubed is constant for every planet in our orbit.
HOMEWORK:
A. Force board and head to tail method can be used to add ectors in 2-D problems.
B. Forces that are not on either x or y axis can be broken in to two forces(one on x axis and another
on y axis). If the force value and the angle is given, resolution of forces can occur using the trig
soh cah toa.
C. Equal liberium is reached when two forces exerted on an object balance out. There is no
movement when reached the equal liberium.
D. Diagonal forces can be split into x axis and y axis. Then, using trig functions, a student simply can
plug the net force value in to Newton’s second law formula.
E. When a student is encountered with an off centered plane questions, simply make diagonal
lines x and y axis. Then, the original horizontal and vertical line will become diagonal line. From
then, everything is the same as the mothod introduced in D.
F. Two system problem solving is harder than a single system because they move or accelerate at
the same rate but different direction. When encountered with these type of questions, split the
two system and work each one out individually.
A. Gravity is a force that pulls objects onto the Earth’s surface. 9.8 m/s/s is the acceleration dueto
gravity.
B. Every object has its own gravitational pull. This is the reason planets orbit the sun. The law of
ilypsis explains that the orbit of planets around the sun, being the one focus, is ilyptical. The law
of equal area says that the distance between the center of the sun and the center of each planet
will carve out the same amount in the same amount of time. The law of harmony=
period^2/average distance from the sun^3.
C. The distance is measured from the center of one to the center of another. As two objects get
farther apart, the gravitational attraction will lessen as well.
D. G is constant for the gravitational attraction(G= 6.67^10^-11). Little g is the acceleration due to
gravity(g=9.8m/s/s).
E.
Day 3:
Changing velocity – changing speed- changing direction
Uniform circular motion- constant speed but changing direction. EF=ma
What’s different is how we find acceleration. We cannot use kinematics.
A c= V2/R
Centripetal acceleration- center seeking
Tention is much bigger in the bottom.
LAB 1:
Part A: Find max tension of string at static equilibrium
Part B: Find min v at top of loop
Part C: Find Max v at bottom of loop
Data table:
Mass (Kg) Radius(m) Revolutions Distance (m) Max Load(kg) Time of period (s) Minimum Velocity (m/s) Average Velocity
0.02
0.37
10
2.325
0.950
6.34
3.667
0.02
0.37
10
2.325
0.950
6.41
3.627
0.02
0.37
10
2.325
0.950
6.5
3.577
0.02
0.37
10
2.325
0.950
6.38
3.644
0.02
0.37
10
2.325
0.950
6.5
3.577
0.02
0.37
10
2.325
0.950
6.54
3.555
3.608
Mass (kg) Radius(m) Revolutions Distance (m) Max Load (kg) Time of preiod (s) Max Velocity (m/s)
Average Velocity
0.02
0.37
10
2.325
0.950
3.77
6.167
6.237
0.02
0.37
10
2.325
0.950
3.72
6.249
0.02
0.37
10
2.325
0.950
3.64
6.387
0.02
0.37
10
2.325
0.950
3.81
6.102
0.02
0.37
10
2.325
0.950
3.7
6.283
0.02
0.37
10
2.325
0.950
3.73
6.233
0.02 0.37 10 2.325 0.950 3.73 6.233
Calculation:
Analysis:
The theoratic and experimental results were too different from each other. The percent error was
approximately 75 pecent. This difference in results came from errors resulting from human’s reaction
time when we pressed the stop watch and also the inability to spin the mass and the string in constant
rate. Data table and calculation are helped by group members. Graphic is from Lawrence because he
had all the calculations.
LAB2:
Conical pendulum
Objective: what happens to the period as you change the radius.
Hypothesis: The radius and the period is inversely proportional to each other.
10 cm radius 4 20 cm radius 1
40 cm radius 2
60 cm radius 3
100 cmradius 5
3.315 s
3.277 s
3.297 s
3.16 s
3.291 s
3.259
2%
Cos =r/l
Cos= 0.10/2.64
Theta= cos-1(0.10/2.64)
Theta= 87.8
V= 2 pie r/period
Solve for period= 2 pie r/v
EFy=may
Ty-w=0
T sin theta= mg
T=mg/ sin theta
0.60%
3.24
3.218
3.142
0.90%
2%
0.50%
g/tan theta=v squared/r
Rg/tan theta=v
(0.10)(9.8)/tan87.8= v squared
0.194 m/s=v
= 2 pie (0.10)/0.194
= 3.238 seconds
0.388 = velocity
Analysis:
This experiment proves that the period and the speed of the ball is inversely proportional to
each other. This lab was done as a clas and the percent error was less than 2 percent. This slight error
results from human’s slow reaction time to press the stop watch. Also the angle at which the students
view the pendulum might have altered the time and thus resulted the wrong data.
HOMEWORK:
Q: What is uniform circular motion?
A: When a circle is a perfect circle with the same radius and when the speed of an object going around it
is constant.
Q: What is the formula for the average speed?
A: The equation is 2pi r/T
Q: What is the relationship between the magnitude of the velocity and the direction of velocity?
A: While magnitude stays the same, the direction might change every second. The best word describing
the direction change of velocity is tangential.
Q: What is the forbidden f word?
A: the forbidden f word is “centrifugl circular motion. This concept is impossible because the object in
circular motion tends to move inward than outward.
Q: What is centripetal circular motion?
A: It is an opposite concept of centrifugal. When an object spins aound, the object has an intuition to
move inward than out ward.
Day 4
Notes:
Work- Three components, work is caused by force acting in the direction of motion of an object and this
object should move. On the axis of direction of motion. The force and the direction of motion cannot be
perpendicular. Symbol: W
Kinetic energy: Energy due to an object moving. Any object that is moving has kinetic energy. Symbol: Ke
Gravitational potential energy: energy possessed by an object because it is above or below zero level. So
it can fall. The zero is relative. Symbol: Gpe
Elastic potential energy: Energy possessed by an object due to a compressed spring or stretched spring.
Symbol: Epe
Units for all of theses is Jouls. J is short hand.
Equations:
Work=force * distance* cos phi. Phi is the angle between force and direction of motion.
Ke= 1/2mv squared
GPE= m*g*h
EPE= ½ little k X squared. K stand for springy your spring is spring force constant. X is the distance it was
compressed or stretched.
Cue for work: tention normal and friction but not weight
Kinetic: if object is moving
Gpe: above or below zero position.
Law of conservation of energy: you have constant amount of energy the types of energy can change but
the total amount must remain constant. The enrgy can be increased by doing work.
Work out is mostly due to friction.