Physics Lab Report Sample

Table of Contents

CHAPTER 1 OBJECTIVE …………...……...………...............................3 | | CHAPTER 2 THEORY …………………………………………………...4 | | CHAPTER 3 PROCEDURE ……………………………………………...7 | | CHAPTER 4 4.1 DATA TABLE ………………………………………...9 | | 4.2 GRAPH ………………………………………………..10 | | CHAPTER 5 ANALYSIS …………………………………………………15 | | CHAPTER 6 ANSWERS AND COMMENTS …………………………..19 | | CHAPTER 7 CONCLUSION……………………….…………………….20 | | REFERENCES …………………………………………….21 | | LAB REPORT RUBRIC …………………………………..22 | |

Chapter 1 Objective
To determine the motion of the cart as it travels down the inverted ramp though the influence of gravitational attraction alone by plotting the velocity per unit-time graph.

Chapter 2 Theory
Motion: In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of velocity, acceleration, displacement, and time. Motion is observed by attaching a frame of reference to a body and measuring its change in position relative to another reference frame. A body which does not move is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in a closed system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum. As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be moving. More generally, the term motion signifies a continuous change in the configuration of a physical system. For example, one can talk about motion of a wave or a quantum particle where the configuration consists of probabilities of occupying specific positions.

Acceleration: In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. Acceleration has the dimensions L T −2. In SI units, acceleration is measured in meters per second squared (m/s2). (Negative acceleration i.e. retardation, also has the same dimensions/units.)
In common speech, the term acceleration is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is anacceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; whereas the rate of change of speed is a tangential acceleration.
In classical mechanics, for a body with constant mass, the acceleration of the body is proportional to the net force acting on it (Newton's second law):

where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration.

Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0.
Average acceleration is the change in velocity (Δv) divided by the change in time (Δt). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Δt approaches zero.
Uniform acceleration: Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period.
A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force, F, acting on a body is given by:

Due to the simple algebraic properties of constant acceleration in the one-dimensional case (that is, the case of acceleration aligned with the initial velocity), there are simple formulas that relate the following quantities: displacement, initial velocity, final velocity, acceleration, and time:

where
= displacement
= initial velocity
= final velocity
= uniform acceleration
= time.
In the case of uniform acceleration of an object that is initially moving in a direction not aligned with the acceleration, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As Galileo showed, the net result is parabolic motion, as in the trajectory of a cannonball, neglecting air resistance.

Acceleration Theory Based On The Experiments

Acceleration is the major physical principle that was tested in the experiment. Acceleration is a vector quantity derived from the product of change in velocity, ∆v and time elapsed, ∆t. Thus the equation for acceleration is∆v/∆t. ∆v in the calculation was obtained by subtracting the initial velocity, vi from the final velocity, vf. As the unit velocity of which acceleration is derived from is a vector quantity; one of which both magnitude and direction is taken into an account, thus the unit acceleration is also dependent on the direction it acts in. In this experiment, the unit of time used was unit time (ut). 1 ut was measured by 5 ticks (space in between two consecutive dots on the ticker tape). The time taken for 1 tick is 0.02 seconds (s). This is due to the frequency of the main power supply in Malaysia being set at 50 Hertz (Hz). That means that within 1 second, the ticker on the ticker timer was ticked a total of 50 times.

Begin End
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* * * * * * * * * * * * * * * * Figure 1.1 – Ticker tape showing positive acceleration
Begin End
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* * * * * * * * * * * * * * * Figure 1.2 – Ticker tape showing negative acceleration

Chapter 3 Procedure
Materials
Frictionless ramp, cellophane tape, ticker tape, meter ruler, graph paper, cart, 12V D.C power supply, ticker timer, blue carbon disc, wooden block,
Variables
Controlled Variable: mass of the ramp, the frequency of the timer, the testing environment, length of ticker tape, the angle of the ramp, height of release
Responding Variable: Acceleration of the cart during the travel down the ramp.

Procedures

1. Set up the apparatus as in the diagram. 2. Connect the ticker timer to a low-voltage (12V) power supply. 3. Using cellophane tape, attach the ticker tape to the rear end of the cart. 4. Align the cart with the ticker timer. 5. Allow the trolley to roll down the runway. 6. The time interval between two adjacent dots is 0.02 s, assuming the ticker timer marks fifty dots per second. 7. Mark out five adjacent spaces along the tape. Measure the length of each adjacent spaces with a meter ruler. 8. Record the measured length in a table. 9. The ticker tape is marked at every 5 intervals recording it as one unit-time (ut). 10. Cut the ticker tape at each the fifth adjacent spaces of each strip which is at each unit-time. 11. The strips are then pasted side by side on a graph paper to form a tape chart. 12. The tape chart is converted into a velocity-time graph. For a body moving in one direction only, the magnitude of its velocity is equal to its speed. 13. A graph of the instantaneous velocity against the unit-time is plotted with the accurate uncertainties. The acceleration is determined by the gradient of the graph. 14. Repeat the experiment.

Chapter 4 Data
4.1 DATA TABLE Unit Time (ut± 0.2) | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | Instantaneous Velocity (cm/ut±0.5) | Set A | 2.1 | 2.6 | 3.0 | 3.5 | 4.0 | 4.5 | 4.9 | 5.5 | 6.0 | 6.4 | Instantaneous Velocity (cm/ut±0.5) | Set B | 4.1 | 4.1 | 4.6 | 5.4 | 6.0 | 6.4 | 6.9 | 7.4 | 8.0 | 8.4 | Instantaneous Velocity (cm/ut±0.5) | Set C | 2.4 | 2.8 | 3.4 | 3.8 | 4.6 | 5.0 | 5.7 | 6.0 | 6.6 | 7.4 | Instantaneous Velocity (cm/ut±0.5) | AverageSet (A+B+C/3) | 2.9 | 3.2 | 3.7 | 4.2 | 4.9 | 5.3 | 5.8 | 6.3 | 6.9 | 7.4 |

4.2 Graph (Computer Generated)

Graph (Ticker Tape Graph)

Graph handed out in hardcopy.

Graph handed out in hardcopy

Graph handed out in hardcopy

Graph of average instantaneous velocity over time graph.

Graph handed out in hardcopy

Chapter 5 Analysis
Error Analysis
After performing the experiment three times there are several errors that can be drawn from it;
Equipment Error: During the experiment there were difficulties that sometimes occurred with the ticker tape timer. Though the machine worked quite effectively the problem was encountered with the blue carbon disc that created imprints on the ticker tape paper. During the experiment on two occasions the disc would either not imprint anything on to the ticker tape paper or come off during that experiment.
Inherent Error: The cart being released and the operation of the ticker tape timer were done by two separate group members. This created the possibility for the cart to be released slightly earlier or later than the ticker tape timer. Though it may not seem significant because the time measurements being recorded are so miniscule such a synchronization problem can significantly change in average velocities per interval.

Data Analysis
Thus velocity corresponds to slope and initial displacement to the intercept on the vertical axis (commonly thought of as the "y" axis). The height of a curve tells you nothing about its slope.
The gradient of the velocity-time gradient gives a value of the changing rate in velocity, which is the acceleration of the object.

Calculating the slope/gradient of the graphs:
The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right. That is:

The gradient of a straight line is denoted by m where:

Therefore: Gradient of the average Set : m= 6.9-2.99-1 = 3.38 = 0.4cm/unit time.

To calculate the uncertainty in the graph, the two gradients (maximum gradient, mmax and minimum gradient, mmin) are then calculated. The uncertainty of the gradient (Δm) is calculated by:
Δm=(m[max] – m[min]) 2

Therefore uncertainty= m[max]= 7.9-2.410-1 = 5.59 = 0.6cm/ut

m[min]= 6.9-3.410-1 = 3.59 = 0.4cm/ut

Δm = 0.6-0.42 = 0.22 = 0.1cm/ut

Chapter 6 Answers and Comments

1. Are the points on the ticker tape equidistant? Explain why.
No, the points on the ticker tape are not equidistant. The wooden trolley accelerates as it moves along the wooden board. As the trolley accelerates, it travels a greater distance within 1 tick, thus the ticker tape gets further and further.

2. What is the unit of acceleration in this experiment?
The unit of acceleration in this experiment is cm/ut. This is because the unit for ∆t is unit time whereas the unit for ∆v is cm.

3. Does the graph suggest a directly proportional relationship between instantaneous velocity and time? Explain how you arrive at this conclusion using the evidence from your graph.
The graph suggests a proportional relationship between instantaneous velocity and time. This because as the time increases, the velocity also increases. The existing amount of deviation suggests that there are some errors in the experiment.

4. Briefly describe how you would calculate the total distance travelled by the car for the first 10.0ut.
The total distance travelled by the car for the first 10.0 ut can be calculated by obtaining the area below the graph from the velocity-time graph. Total Distance Traveled=Area Under Graph.

5. Suggest possible improvements to the experiment to achieve a more accurate results. There are two major improvements that can be proposed to make the data collected from this experiment more precise and accurate. The first improvement would be the creation of a tool to allow one person to operate both the ticker tape timer and release of the cart. By creating a release button that would operate both devices it would synchronize them and ensure the data was precise. Also placing groove on the board which the car could run along on the ramp would allow the car to have a constant start and end track on the board. This would eliminate the variation of places the car could start and finish from and the chance of the car falling of the board near the end of its run.

Chapter 7 Conclusion
As a conclusion, the motion of the cart as is moves down the ram in an acceleration motion. The results obtained indicate a directly proportional relationship between instantaneous velocity and time. The acceleration of the trolley is 0.4 ± 0.1cm/unit time.

References
Benson, Tom. 2011. Newton’s Second Law. National Aeronautics and Space Administration. Accessed April 22 2012. http://www.grc.nasa.gov/WWW/k-12/airplane/newton2.html

Cranfield University 2012. http://www.racemath.info/motionandenergy/velocity_time_graph_a.htm

Elert, Glenn. 1998. Work. Accessed April 23 2012. http://physics.info/work/

Feimer. 2012. Study Of Motion - "Ticker Tape": Observations and Measurements. 3M&D,inc. Accessed April 22 2012. http://www.physicsphenomena.com/TickerTape.html

Foster, Niki. 2012. What is Gravity?. Accessed April 22 2012. http://www.wisegeek.com/what-is-gravity.htm

Henderson, Tom. 2012a. 1-D Kinematics : Describing Motion with words. The Physics Classroom Project. Accessed April 22 2012. http://www.physicsclassroom.com/ Class/1DKin/U1L1e.cfm

Crew, Henry .2008. The Principles of Mechanics. BiblioBazaar, LLC. pp. 43. ISBN 0559368712.
Bondi, Hermann. 1980. Relativity and Common Sense. Courier Dover Publications. pp. 3. ISBN 0486240215.
Brian Greene, The Fabric of the Cosmos, page 67. Vintage ISBN 0-375-72720-5.