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Folded Corner: One-on-one tutoring is available for Phys140 (lecture). To request a tutor go to http://www.upj.pitt.edu/285/.
If you have trouble getting a tutor please contact Beta Keramati (keramati@pitt.edu) ENERGY – BALL TOSS

In this experiment you saw that the kinetic energy and the gravitational potential energy are both parabolic functions of time. Let’s see if we can explain why.

Kinetic Energy

Since throughout its motion the ball has constant acceleration, its velocity is .

Therefore, one can write KE as a function of time as

This shows that KE is a quadratic function of time. Therefore the graph of KE vs time should be a parabola.

Gravitational Potential Energy

U_g = mgy Since this is motion with constant acceleration

Therefore, we can write U_g as a function of time the following way:

U_g=

This shows the gravitational potential energy is also a quadratic function of time, and its graph should also be a parabola.

This shows that KE is a quadratic function of time. Therefore the graph of KE vs time should be a parabola.

ENERGY – SPRING-MASS SYSTEM

In this experiment the motion detector must be zeroed at the equilibrium position of the mass. This means, you had to wait long enough for all oscillations to stop and then zero the sensor. If this is done properly, the graph of position vs time comes out to be perfectly symmetric about zero. And the graph of potential energy vs time would have even peaks.

The following is a sample of what was expected.

To better understand these graphs, you need to print them out and use a ruler to line up some of the points. For example, notice that when the object is farthest away from the equilibrium position, the elastic potential energy is maximum, while the kinetic energy is zero. As the object moves down toward the equilibrium, its elastic potential energy decreases, while it gains kinetic energy. When it passes the equilibrium point, the object’s elastic potential energy is zero, while its kinetic energy is maximum. Finally, as the object moves below the equilibrium point, the elastic potential energy goes up, while the kinetic energy goes down. At its lowest point, the object has its maximum elastic potential energy and no kinetic energy.

Also notice the black line that represent the Total Energy which is the sum of the kinetic and elastic potential energy at any given instant. Notice the total energy stays constant throughout the oscillation, indicating that the total energy of the system is conserved.

VERTICAL JUMP

If you need to make correction to this report, please use this blank worksheet for all your corrections. Please DO NOT change anything on the original report. Thanks.

PROJECTILE MOTION

In order to analyze projectile motion we have to break it up into two parts – horizontal part, and vertical part. Similarly, to draw motion diagram for a projectile, we must draw two sets of diagrams and separate the horizontal motion from the vertical motion. Consider the case where a ball is shot horizontally. The motion diagrams look like this:

If the ball is projected at an angle above horizontal, then the ball initially goes up and then comes back down. To show this, we draw the motion diagrams as following:

REPRESENTATIONS OF MOTION

There are only two types of motion that we study in detail in this course- (1) motion with constant velocity, and (2) motion with constant acceleration. You must know the shapes of the graphs of position vs time, velocity vs time, and acceleration vs time for these two types of motion in various circumstances. The lab was designed to help you explore these graphical features. I used the same set up you used to generate the following graphs. Please note the shape of each graph and make sure you know how to interpret it.

Click on the links below to see the graphs	Description of Motion
Constant positive velocity	Cart moving away from motion detector at a steady pace
Constant negative velocity	Cart moving toward the motion detector at a steady pace
Constant positive acceleration – speeding up	Cart moving away from motion detector and speeding up
Constant positive acceleration – slowing down	Cart moving toward the motion detector and slowing down
Constant positive acceleration – slowing down, then speeding up	Cart moving toward the motion detector and slowing down, stops, turns around and moves away while speeding up
Constant negative acceleration – speeding up	Cart moving toward the motion detector and speeding up
Constant negative acceleration – slowing down	Cart moving away from the motion detector and slowing down
Constant negative acceleration – slowing down, then speeding up	Cart moving toward the motion detector and speeding up, stops, turns around and moves toward the motion detector while speeding up

KINEMATICS GRAPHS

These are the movies of the fan cart slowing down and speeding up in positive and negative directions.

SloAway SpeedTo SloToward SpeedAway

From each movie you can take data and plot a graph of position vs time. The modeling feature of the player allows you to curve-fit the data points.

To begin collecting data, click on the dot on the left side to “view data points”, then track the motion of the cart by clicking the red dot on the cart with the target. Click the ruler on the left to “set the scale”. To curve-fit the data points, click on “M” on the right side of the screen and choose “Quad” for a quadratic function

(, then move the two blue circles to find the curve that best fits the data points. The equation of the curve appears at the bottom of the screen.

WRITING LAB REPORTS

Depending on the nature of the experiment and the amount of time available, students will either write a complete lab report, or answer specific questions in a hand-out. A complete lab report must be written in the format outlined below.

Name                                                                                Partners

                                                                                          Date

Title of the Experiment

Introduction

The purpose of the experiment,

Description of the set up,

Brief explanation of the general process (what will be measured and how).

Body

·         Raw data presented in an organized fashion in a data table and accompanied by appropriate units.

·         Calculations.

·         Units and uncertainties must be carried through all calculations.

·         All uncertainty calculations must be included in detail.

·         A clear record of your thought process. This should include an interpretation of what you calculated. Graphs and other presentations and analysis of data.

Conclusion

Report the final result along with its uncertainty and percent error.

An interpretation of the general results of the experiment.

If applicable, compare % uncertainty with %error (or %difference) and comment on the extent to which your results agree (or don’t agree) with what you expected to get.

Discuss possible sources of error and, if applicable, include suggestions for improving the experiment.

Please keep in mind that a good lab report is written such that another person can use it to reproduce the experiment and get the same results. Keep your report concise (you don’t need to write pages after pages. Make an effort to write efficiently) and complete (be sure to include all relevant information to convey clearly what you did, how you did it, and what it means).

This sample lab report illustrates the format that I expect to see in your reports.

EVALUATION AND GRADING OF LAB REPORTS

Lab reports are submitted for evaluation at the end of each lab. I will read your report and if necessary give you suggestions for improvement without assigning a grade. You will resubmit your report with corrections. The corrected report will receive a grade.

GUIDELINES FOR MAKING CORRECTIONS TO LAB REPORTS

1. Do not erase or change the original report.

2. Use a different color to make small corrections (units, significant figures, etc.) on the original report.

3. More extensive corrections (rewriting a paragraph, redoing calculations, etc.) should be done on a separate sheet of paper and attached to the original report.

4. Place all your completed reports in a folder with pockets and turn them in by the dates indicated below.