Motion

In this lab you will analyze and describe motion with a constant velocity and motion with a nonconstant velocity. For all experiments you will be using a low friction cart on a track and a motion detector connected to the computer (Fig. 1). As the cart is moved the motion detector tracks the distance of the cart at a set time interval and creates a graph of time vs. distance (Fig 2).

Figure 1

Figure 2

There are four different graphs you will generate. Be sure to draw all of the graphs you generate and understand how you created each one. Also, check the slope of the graphs you create-your instructor will show you how to do this.

***Changing the height of the ramp does not result in a new graph. Also, always release the cart from one end or the other NOT the center of the ramp.***

Free Fall

An object in free fall moves toward the earth with a uniform accelerated motion due to gravity. In this experiment, you will be calculating the acceleration, g, of an object in free fall and comparing it to the known value for g.

On your table you should see an experimental setup looking something like the following figure.

1. Your assembly will be missing the paper strip with the mass-you will have to add this using the following method. Tear off a piece of the paper strip that is about 4 ft. in length. At one end attach a mass. Feed the other end of the paper through the ticker-notice in the figure, the paper must go under the metal bar, but over the circle of carbon paper or no dots will be produced.

2. When you are ready to run the experiment pull the paper strip up through the ticker until the mass is about an inch from the ticker. Hold the paper as straight up as possible. Turn the switch on the front of the ticker to 40 Hz and after 2-3 seconds release the paper strip. As the paper falls, small dots will be made on the underside of the paper.

3. Turn over the paper strip and locate your 3^rddot and make a straight line through this dot to serve as your reference line for measuring the distance to the other dots.

4. Measure the total distance of each dot from the reference line and record in the table below

5. For each mark record the total time elapsed at each mark. The first mark would be 40 Hz or 1/40 second, the second would be 1/40 plus 1/40 or 2/40 (0.05s). Put each of these times in the table below.

6. Using the equation provided with the table below, calculate the velocity at each mark and record this in the table.

7. Repeat the experiment using a different mass.

Results

1. Using SPSS, run a regression analysis on your data using time and velocity as your factors. Which one is the independent variable? Dependent?

2. What is the slope of your line? What does this value represent?

3. Use your calculated value of acceleration and the accepted value and calculate the experimental error.

4. What factors may have affected your acceleration?

Dot Number	Distance (cm) Sample 1 _________g	Distance (cm) Sample 2 __________g	Time of Fall (s)	Computed Instantaneous Velocity (cm/s)** Sample 1	Computed Instantaneous Velocity (cm/s)** Sample 2
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Newton's 2nd Law

Objective

To investigate the relationship between motion, mass, and force stated in Newton's Second Law.

Apparatus

low friction car and track, smart pulley, ULI interface, computer, string, hanging masses, ruler, balance

1. What is the equation for Newton’s second law? Which of these factors can you control? How?

2. What additional force must be considered when calculating the net force? (Hint: how are you achieving acceleration?)

3. Write a null hypothesis for this experiment

Total Mass (kg) (car + masses + hanging)

Car mass + mass in car (kg)

Hanging mass (kg)

Acceleration (m/s^2)

Net Force (hanging mass * 9.8 m/s^2)

Plot the variables for Newton's Second Law to see if there is a relationship between moving mass (system mass, car and hanging mass), acceleration, and net (unbalanced) force. It may help to rearange Newton's Second law equation so it is in the form of y=mx+b matching what you plotted.

Follow-up Questions:

1. How do you know if acceleration was proportional to the force?

2. How would you know if the acceleration was inversely proportional to the mass?

3. Would the presence of an additional mass in the cart during all the runs increase, decrease, or not affect the slope? How could you use this experimental set-up to find the value of the additional mass that was in the cart?

4. Suppose the string breaks as the cart accelerates one-third of the way across the track. What is the acceleration of the cart for the remaining length of track? Explain.

Projectile Motion

You have been asked to help out the Cincinnati Bengals quarterback in determining the best speed and angle of release of the football to achieve maximum distance. Currently he is having difficulty determining how best to achieve max distance and they have lost several recent games as a result. You need to design an experiment looking at projectile motion and determine how distance is related to angle and speed.

Equipment Available: Small cannon with:

3 speed settings

multiple angle settings

metal ball

1. Please write your null hypothesis for this experiment

2. Please describe your methods for conducting this experiment

3. How will you plot your data? Use SPSS to create a plot of your data and be sure to label the axes

4. What advice would you give the quarterback on how to throw the ball for maximum distance?

5. Check out the following website and see if your data agree. http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html