Ch2_hwangt

toc = Chapter 2 = 9/7/11

1-D Kinematics - Lesson 1
a.) Mechanics - the study of the motion of objects Kinematics - the science of describing the motion of objects using words diagrams words, diagrams, numbers, graphs, and equations b.) 2 things that I understood well was that the motion of an object can always be described by words such as a car going fast and also the difference between scalars and vectors. The difference between vectors and scalars is that vectors are quantities that are fully described by both a magnitude and a direction while scalars are quantities that are fully described only by a magnitude.
 * Kinematics is a branch of mechanics
 * goal of kinematics is to develop sophisticated mental models that serve to describe the motions of real-world objects

c.)Distance - a scalar quantity that refers to "how much ground an object has covered". Displacement - a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. d.)Speed - a scalar quantity that refers to "how fast an object is moving" Velocity - a vector quantity that refers to "the rate at which an object changes position" Average speed = distance traveled/time traveled Average velocity = the change is position/time = displacement/time Did not have any questions. e.)Acceleration - a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. Acceleration deals with the change in speed or velocity. Constant acceleration is when the change in velocity is consistent between each interval. Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value. Acceleration can be calculate by the following formula: a = (V f - V i )/ delta t. The equation can be written in other ways to adjust to what a problem is asking The direction of an acceleration vector depends on whether the object is speeding up or slowing down and whether the object is moving in a positive or negative direction. The general rule of thumb is that if an object is slowing down, then its acceleration is in the opposite direction of its motion.
 * a vector quantity is direction-aware
 * a scalar quantity is ignorant of direction

__In Class Notes on Speed and Motion Diagrams 9/8/11__
9/8/11 Average speed - the total average of speed traveled Constant speed - speed that is unchanging instantaneous speed - speed traveled at that instant (speedometer)

__Motion Diagram__ At rest - V=0 and a = 0

Constant speed - -->-->--> a=0

Increasing speed - -->>-->, a=-->, acceleration points in the same direction as velocity

Decreasing speed - -->>-->, a=<--, acceleration points opposite direction from velocity

1-D Kinematics - Lesson 2
a.) b.)Ticker tape diagram A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time. The object moves and drags the tape through the ticker and leaves a trail of dots. The trail of dots provides a history of the object's motion and therefore a representation of the object's motion.
 * The world that we study is physics is the physical world or a world that we can see and use our other senses. If we can see something, then we can visualize it, and if we understand it, then we should be able to involve visual representation as we understand each thing.
 * One should always think about one's ability to visually represent something
 * A person should always have his understanding of physics intimately tied to the physical world
 * 2 ways of describing motion are by a ticker tape diagram and a vector diagram

Picture shows whether the object is moving fast or slow



Shows whetherthe objects speed is )onstant or whether it is accelerating.

c.) Vector Diagrams Vector diagrams are diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow. It can be used to describe the velocity of a moving object during its motion.

Size of arrows show whether the velocity is constant if the arrows are all the same length or it the velocity is increasing or accelerating if the arrows grow bigger each time.

The Speed of a Constant Motion Vehicle Lab
Objectives:
 * 1) How precisely can you measure distances with a meter-stick?
 * 2) How fast does my CMV (constant motion vehicle) move?
 * 3) What information can you get from a position-time graph?

Materials: spark timer, spark tape, meter-stick, masking tape, CMV Hypothesis:
 * 1) A meter-stick can measure something as small as a millimeter and as big as one meter.
 * 2) My CMV can go about 1 foot per second.
 * 3) A person can find whether an object has a constant velocity or whether the object is accelerating and also the actual speed of the the object.

Data table: Position Vs. Time



Analysis:
 * They y is the change in position
 * The x is the change in time
 * The slope is the velocity of the CMV.

Discussion Questions: Conclusion: As a result of the experiment, the CMV went about 55 centimeters per second. My hypothesis was that for each second the CMV would go 1 foot but I was wrong. There were many things that contributed to inaccuracy. Some things that could have caused the error was that the surface was not always level, the 0 point may not have stayed at 0, and because we had to judge how many of the first dots we had to take off. To minimize errors on the experiment, a person could you tape measure instead of a meter stick. Also a person could get more information than they already have so that that person can get an even more accurate answer.
 * 1) The slope in a position time graph is equal to the velocity because the slope is the speed of the CMV which is also the velocity.
 * 2) It is average velocity and not instantaneous velocity because instant velocity is just from point to point but average velocity is the the average of all the different velocities and since we have more than one point, we need to used average velocity.
 * 3) It is okay to set the y-intercept to zero because we are start to collect data at zero.
 * 4) The R 2 value is how accurate the data is to the line of best fit.
 * 5) I would expect it to be lower and have a smaller slope than my original graph.

Activity: Graphical Representation of Equilibrium


At Rest

Constant Slow

Constant Fast

Discussion Questions: Constant speed: an object moves at one speed through out its entire journey.
 * 1) In a position vs time graph, the line has no slope and is going straight across the graph a little above the 0 since a person cannot be on top of the motion sensor. In a velocity vs time graph, the velocity is at 0 since your not moving. In an acceleration vs time graph, the line is at 0 since your not moving.
 * 2) To tell you motion is steady, the position vs time graph has a constant slope, the velocity vs time graph stays around one number constantly, and the acceleration vs time graph stays at 0 since the velocity is constant.
 * 3) A person can tell whether an object is moving fast or slow on a position vs time graph by looking at the slopes of the two lines. The steeper slope is the faster moving object and the one with the not as steep slope is the slower moving object. In a velocity vs time graph, the velocity for the faster object is higher above or lower than the slower moving object depending if the objects are moving towards or away from the motion sensor. For a acceleration vs time graph, a person cannot tell whether or not an object is faster than another object since the acceleration is at 0 for both objects since they are not going any faster than they already are.
 * 4) In a position vs time graph, the line has a positive slope if the the object is moving away from you and the line has a negative slow if the object is moving toward you. In a velocity vs time graph, the line is above zero and stays constant at one number if the object is moving away from you and the line is below zero and stays constant at one number if the object is moving toward you. In a acceleration vs time graph, a person cannot tell if the object is changing directions since at constant speed the acceleration is 0.
 * 5) A position vs time graph can tell a person if the object is close by or far away and also whether the object was moving toward or away from you. From the graph you can tell what the total distance that the object traveled, the displacement of an object, and also the average speed of the object by looking at the slope if the object was moving at a constant speed. A velocity vs time graph can tell you whether an object is moving at a constant velocity, at rest, or if an object is accelerating or slowing down. A line above zero shows an object moving away from you and a line below zero shows an object moving toward you. An acceleration vs time graph shows constant speed or acceleration.
 * 6) In a position vs time graph, a person is unable to see the instantaneous speed. In a velocity vs time graph, a person cannot tell the position of object. In an acceleration vs time graph, a person cannot tell what the position is or what the velocity is.
 * 7) No motion: an object is at rest or is not moving.

Cart Graphing Activity


Decreasing Towards and Away Increasing Towards and Away

1-D Kinematics: Lesson 3
a.) The shapes of the graphs shows 2 different motions - constant velocity and acceleration motion. The slopes of the graphs reflect the behavior of the velocity and the velocity exhibits the same characteristics as the slope. If the velocity is changing, then the slope is changing and if the velocity is constant, then the slope is constant. Slow, rightward positive constant velocity; fast, rightward positive constant velocity; slow, leftward negative constant velocity; fast, leftward negative constant velocity; negative velocity from slow to fas Leftward negative velocity from fast to slow b.) The slope of a position vs time graph shows a person the velocity of the moving object. A small slope means low velocity, negative slope means negative velocity, a constant slope means the the object has a constant velocity, and a changing slope shows that the velocity is constantly changing. if the velocity of the object being recorded is 4 m/s then the slope will be 4. If the velocity is at 0 m/s then the slope is 0. This graph here shows a constant slope. That means that the object that is being recorded has a constant velocity, in this case 10 m/s.

c.)Knowing how to calculate slope is essential for a student taking physics. This equation tells us how to find the slope of a line by taking one y value of a coordinate on a line being subtracted by another y and then divided by the corresponding x of the first y subtracted by the corresponding x of the second y. These example give us an idea of how to find slope.

1-D Kinematics - Lesson 4
In a velocity vs time graph, the shape of the line shows whether the velocity is constant, increasing, or decreasing. One can also tell whether an object is moving towards them or away from them. This graph shows positive velocity and zero acceleration This graph shows positive velocity and positive acceleration. The slope of a line on a velocity vs time graph shows information on acceleration. If acceleration is positive then the slope of the line on a v-t graph is positive and if the acceleration is negative then the slope is negative. The slope of a v-t graph shows if an object is accelerating, is constant, or is at rest. There three graphs show how motion is related to the shape of the graph. Like the x-t graph, one can find the slope of a v-t graph using the same equation. The area of a v-t graph can be found out by using length times width for a rectangle, (1/2)base times height for a triangle, and (1/2)base times (height one plus height two)

Cart On An Incline Lab
Objectives:
 * 1) What does a position-time graph for increasing speed look like?
 * 2) What information can be found from from the graph.

Hypothesis:
 * 1) On a position-time graph, the slope of the line goes grows larger as you go from left to right.
 * 2) A person can find where the cart is at a certain point in time and also the velocity of the moving object.

Procedure: Data Table for Acceleration of Cart Analysis: a.) In my equation, which was y = 13.114x 2 + 24.279x, the initial velocity was the y - intercept value, the b value or 24.279. The a value or 13.114 is the 1/2 the acceleration since my equation can be represented as delta d = V i t + 1/2at 2 and you can replace the numbers for V i and 1/2a. Since 13.114 is 1/2a, you need to double it to get the acceleration. b.)The instantaneous velocity at the halfway point is 37.5 cm/s and the instantaneous velocity at the end is 53.3 cm/s. c.)The average speed is 37.7 cm/s.
 * Set up spark timer at the top of the incline.
 * Run the spark tape through the spark timer and tape it to the cart
 * Turn on the spark timer and let the cart go down the incline.
 * Measure the distance between 11 dots on the spark tape and record data.
 * Move timer to the bottom of incline and record data by pushing the cart up the incline.
 * Cut off any part that is increasing in speed and measure distance between 11 dots.

Discussion Questions:
 * 1) If the incline was made steeper, the curve of the x-t graph would also grow steeper since the cart gains more speed with a steeper incline.
 * 2) If the cart was decreasing up the incline, it would start out fast and then start to slow down. The shape of the graph would start out steep and then start to flatten out towards the end.
 * 3) The average speed is a little less than half the instantaneous speed at the halfway point.
 * 4) This makes sense because the slope of the tangent line will not change and gives the speed at that exact point in time so a person is also able to say it is the instantaneous speed.
 * 5) [[image:Screen_shot_2011-09-21_at_5.57.05_AM.png width="561" height="282"]]

Conclusion:

A Crash Course in Velocity Lab
9/25/2011 Done by Timothy Hwang and Maxx Grunfield Our car - 58.021 cm/s, other car - 31.875 cm/s Objectives:
 * 1) Find the position where both CMV’s will meet if they start //at least// 600 cm apart, move towards each other, and start simultaneously.
 * 2) Find the position where the faster CMV will catch up with the slower CMV if they start //at least// 1 m apart, move in the same direction, and start simultaneously.

Hypothesis:
 * 1) (V1 + V2)t = D
 * 2) (58.021 + 31.875)t = 600
 * 3) t = 6.67s
 * 4) V = d/t
 * 5) 58.021 = d1/6.67
 * 6) d1 = **387 cm**
 * 7) d2 = **213 cm**
 * 8) V1 = d1/t1
 * 9) 31.875t = d1
 * 10) d = V i t + 1/2at 2
 * 11) d1 + 100 = 58.021t + 1/2(0)t 2
 * 12) 31.875t + 100 = 58.021t
 * 13) t = 3.82s
 * 14) d1 + 100 = **221.8 cm**

Materials: 2 constant motion vehicles, another lab group, tape measure and/or meter stick, and camera

Procedure: media type="file" key="1 M Overtake-1.mov" width="300" height="300" media type="file" key="600 CM Crash Course-1.mov" width="300" height="300"

Data: Crash - Catching up -

Analysis: Sample Calc of % Error - ((213-220.04)/213)100 = -3.31%

Sample Calc of % Difference - ((236.094-221.040/236.094)100 = 6.80%

Discussion Questions:
 * 1) If the cars' speeds were equal to one another, the distance that both cars would travel would be 300 cm in the crash part of the lab since they have the same speed. If one was finding out where one catches up to the other, there would be not answer. Since in order to catch up to another object, one needs to be faster than the other but since they are both going at the same speed, one will no catch up to the other.
 * 2) [[image:photo-3.jpg]]
 * 3) [[image:photo-2.jpg]]

Conclusion: In the lab, I hypothesized that the two cars would crash at about 213 cm at 6.67s in the first scenario and in the second scenario, the faster car would catch up to the slower car at about 221.8 cm at 3.82s. In the lab, some of the measurements we had were way off what we had originally expected but most of the measurements we found were close to one another. This was probably due to letting go of the cars at different times, the car turned while moving, the measurements being close estimate and not exact measurement, and many others as well. These imperfections could be solved by saying a count off and the letting the cars go at zero or maybe fixing the car so that it went straight instead of tilting. One can also solve the problem by getting a straight edge, putting it on the tape measure where we theroized the two cars would crash or meet, and moving it from left to right to accommodate for other errors.

Egg Drop Project
Description of final project: So for our final project, we took 2 sheets of paper, made a cone out of them, and taped them together so that it would catch a lot of air and slow the project down. Our prototype had a square parachute and that did not work out so well. It did not slow down enough for the egg to land safely on the ground. The container that held the egg is made of straw and has a crumpled piece of paper to cushion the egg as it hit the ground. The egg is wrapped in a piece of paper for precautionary measures so that it has an extra cushion and the container is connected to the parachute with 4 pieces of thread. Results: The egg landed on the ground intact.

Analysis: d = 8.5 m t = 2.25 s v i = 0 m/s a = ?

d = v i t + (1/2)at 2 8.5 = 0(2.25) + (1/2)(2.25)a a = 3.36 m/s 2

Comparison to Acceleration of Gravity (9.8 m/s 2 ): The acceleration of a free falling object is 9.8 m/s 2 because that is the acceleration of gravity but with how project, we were able to slow down the acceleration to 3.36 m/s 2 by using a parachute and the egg did not crack.

Things I would have done differently: I would probably try to make it a bit lighter than it was so that the project would land a little slower than it did. Putting paper around the egg and putting all that paper at the bottom could have been superfluous. If I took some of the paper out it may still have worked and had a slower acceleration. However, my final project was a success and I liked doing this lab. It was fun.

Free Falling Class Notes
Free fall - any object only acting on by the force of gravity acceleration = 9.8 m/s2

1-D Kinematics Lesson 5
a.) A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects:   Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a [|ticker tape trace] or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an [|earlier lesson], that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminates the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right.
 * Free-falling objects do not encounter air resistance.
 * All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for //back-of-the-envelope// calculations)

b.) It was learned in the [|previous part of this lesson] that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s/s. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s/s in The Physics Classroom Tutorial in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s/s, downward

( ~ 10 m/s/s, downward)

c.) In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs.A position versus time graph for a free-falling object is shown below.

Observe that the line on the graph curves. [|As learned earlier], a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object ([|as learned in Lesson 3]), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. A velocity versus time graph for a free-falling object is shown below.

Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the [|vector nature of acceleration]). Since the slope of any velocity versus time graph is the acceleration of the object ([|as learned in Lesson 4]), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction.

d.) Free-falling objects are in a state of acceleration. Specifically, they are accelerating at a rate of 9.8 m/s/s. This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. If dropped from a position of rest, the object will be traveling 9.8 m/s (approximately 10 m/s) at the end of the first second, 19.6 m/s (approximately 20 m/s) at the end of the second second, 29.4 m/s (approximately 30 m/s) at the end of the third second, etc. Thus, the velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is  ** vf = g * t **  where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest. Example calculations for the velocity of a free-falling object after six and eight seconds are shown below. ** Example Calculations: ** At t = 6 s

vf = (9.8 m/s2) * (6 s) = 58.8 m/s At t = 8 s

vf = (9.8 m/s2) * (8 s) = 78.4 m/s The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula. ** d = 0.5 * g * t2 ** where g is the acceleration of gravity (9.8 m/s/s on Earth). Example calculations for the distance fallen by a free-falling object after one and two seconds are shown below. ** Example Calculations: ** At t = 1 s

d = (0.5) * (9.8 m/s2) * (1 s)2 = 4.9 m At t = 2 s

d = (0.5) * (9.8 m/s2) * (2 s)2 = 19.6 m At t = 5 s

d = (0.5) * (9.8 m/s2) * (5 s)2 = 123 m

(rounded from 122.5 m) The diagram below (not drawn to scale) shows the results of several distance calculations for a free-falling object dropped from a position of rest.

e.) Earlier in this lesson, it was stated that the acceleration of a free-falling object (on earth) is 9.8 m/s/s. This value (known as the acceleration of gravity) is the same for all free-falling objects regardless of how long they have been falling, or whether they were initially dropped from rest or thrown up into the air. Yet the questions are often asked "doesn't a more massive object accelerate at a greater rate than a less massive object?" "Wouldn't an elephant free-fall faster than a mouse?" This question is a reasonable inquiry that is probably based in part upon personal observations made of falling objects in the physical world. After all, nearly everyone has observed the difference in the rate of fall of a single piece of paper (or similar object) and a textbook. The two objects clearly travel to the ground at different rates - with the more massive book falling faster.  The answer to the question (doesn't a more massive object accelerate at a greater rate than a less massive object?) is absolutely not! That is, absolutely not if we are considering the specific type of falling motion known as free-fall. Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present.

The actual explanation of why all objects accelerate at the same rate involves the concepts of force and mass. The details will be discussed in Unit 2 of The Physics Classroom. At that time, you will learn that the acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. Thus, the greater force on more massive objects is offset by the inverse influence of greater mass. Subsequently, all objects free fall at the same rate of acceleration, regardless of their mass.

Free-Fall Lab
Lab Partner: Maxx Grunfeld Objectives: What is acceleration due to gravity? Hypothesis: The acceleration is 9.8 m/s 2. The v-t graph will look a diagonal from 0 going downwards. You can find the acceleration of the object on a v-t graph by finding the slope of the the line. Materials: spark timer, spark tape, mass, masking tape Procedure:
 * 1) tear off a long piece (that is not crumpled) of spark tape
 * 2) thread the spark tape through spark timer and tape the spark tape to the mass
 * 3) hold the spark timer and let the mass go
 * 4) Get at least 10 dots on the tape

Mass of object = 100g

Data of Position vs Time Graph:

Data of Velocity vs Time Graph:

Whole Class Data:

Analysis: The curve of the position vs time graph shows that the mass that we dropped from the balcony was increasing in speed. The trendline equation, y=583.67x 2 -26.011x, when compared to the equation ∆d=v i t + (1/2)at 2, shows that 583.67 is half the acceleration and that -26.011 is the initial velocity. The R 2 value shows how close it was to being 100% accurate and our graph was 98.4% accurate. The straight line in the v-t graph shows that there was a constant acceleration. The equation was y=805x+60.036 with an R2 value of .99909. The 805 represents that slope and the acceleration of the the mass in cm/s 2. The y-int is 60.036 and not at 0 because we did not drop the mass right when the spark timer clicked. We left out our last velocity in our graph because there was too big a gap between the last two points and made the R 2 value very low. After taking the last point off, we got what we have now.

% Error =17.9% % Difference =3.48%

Sample Calcs:
 * Velocity (tangent is on .4 seconds)
 * V = ∆D/∆T
 * V = (125-43)/(.5-.3)
 * V = 410 m/s
 * % Error
 * % Error = ((theoretical-experimental)/theoretical)*100
 * % Error = ((981-805)/981)*100
 * % Error = 17.9%
 * % Difference
 * % Difference = ((average experimental value-experimental value)/average experimental value)*100
 * % Difference = ((834.03-805)/834.03)*100
 * % Difference = 3.38%

Discussion Questions:
 * 1) Yes, the shape of the v-t graph does agree with the expected graph because a straight line with a constant slope shows a constant acceleration.
 * 2) Yes, the shape of the x-t graph does agree with the expected graph because the curved line shows how velocity is increasing over time, which shows acceleration.
 * 3) Compared to the other results of the class, our result was more to the lower side but was still fine. Our results were still clustered in the same area. We had a percent difference of 3.38% which means that our result was very close to the class average.
 * 4) Our object did accelerate uniformly because the straight line on the v-t graph shows that the acceleration was constant and uniform.
 * 5) The acceleration due to gravity could be higher that 9.8 m/s2 if there was another force pulling the object down or if the spark tape was crinkled, there could be a skipped dot so the acceleration would be higher. The acceleration could be lower if there was something slowing it down like friction.

Conclusion: Our hypotheses were correct but our results were not as we expected. Our acceleration was 805 cm/s2 when the acceleration of gravity is 981 cm/s2. Our acceleration was actually much slower than the actual acceleration of gravity. There was a 17.9% error between our acceleration and the acceleration of gravity. This could have been do to friction when the spark tape was going through the spark timer. The friction could have slowed down the acceleration and therefore cause the object to fall as a slower rate. To prevent it from happening again, the other partner that is not holding the spark timer should told the spark tape up high so that there is less friction to slow the mass down.