Newton’s Second Law

PURPOSE: To investigate Newton’s second law of motion.

THEORY: Newton’s second law of motion states that when an unbalanced force acts on an object the object will accelerate. The equation that relates the force F. Mass m, and the acceleration a is: F = m a. With a car setting on the air track the weight is being balanced by the normal force of the track pushing up.

The force causing object one to accelerate is the unbalanced force with which the string is pulling on the car. This force is T₁. The net force acting on object two is W₂ - T₂. The equations of motion for the two objects are T₁ = m₁a₁ and m₂g - T₂ = m₂a₂. If the string does not stretch then the change in position of object one to the right is the same as the change in position of object two downward. Therefore a₂ = - a₁ or if a₁ = a then a₂ = - a. Also if the string is light (massless) and the tension in the string is everywhere the same, then T₁ = T₂ = T. The equations of motion for the two bodies then becomes T = m₁a and T - m₂g = - m₂a. Solving the two simultaneous equations for T and a.

EQUIPMENT: Computer and VideoPoint software.

PROCEDURE: There are several video files from which to chose. From the "PASCO" subdirectory chose one of the following: pasco88, pasco89, pasco90, pasco91, pasco92,

and pasco93. With the VideoPoint software mark the position of the object as it accelerates. There is a step-by step procedure at the end of the laboratory for using VideoPoint for this experiment. You should have reviewed the introduction provided with the VideoPoint CD and the Walkthrough on the CD or the Web sight. This data can be copied into the provided data table. Make a graph of velocity verses time and find the slope of the velocity verses time graph . This slope is the acceleration of the masses. The masses of the objects in the experiment are given on the first frame of the video. Compare the acceleration found from the graph to that calculated from the formula above and find the percent error in agreement of these two values. Treat the experimental value as the expected value.

STEP - BY - STEP Procedure for VideoPoint

Start VideoPoint.

Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.

In the "open" dialogue box do the following.

Select the drive letter of the CD drive in which VideoPoint is located.

Select movies folder and the appropriate folder under movies (here the "pasco" folder).

Under filename select the appropriate file to be loaded.

Press "OK".

The "Number of points" dialogue box will appear. Make sure "1" is selected and press "OK". The movie and software should now be loaded.

Record the masses listed in the first frame of the movie.

On the menu bar select "Movie" and "Full Screen" using the left mouse button.

Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on a point on the top cart and press the left mouse button, the movie will advance one frame and the data is recorded. Repeat this process until all frames of the movie have been used. Be consistent and use the same point on the cart each time to record the data. Ignore any carts moving on lower tracks, they can be used for relative velocity experiments.

Calibrate the movie.

Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.

The "Scale Movie" dialogue box appears. Select continue with the left mouse button.

Put the target cursor on the left end of the meter stick in the first movie frame and press left mouse button - repeat for the right end of the meter stick.

On the menu bar select "Movie" and "Normal Size".

Graph the data.

Select "Graph" tool button on tool bar at left side of the window with left mouse button. (8th button from top) - "Plot Series" dialogue box will appear.

The horizontal axes should be "time".

The vertical axis should be "Point S1" and "X".

The position, and velocity options should be highlighted by clicking the left mouse button when the cursor is on the word.

Press "OK" and the graphs should appear.

Fit equations to the graphs.

With cursor on each graph click left mouse button then select the "F" flag and click left mouse button again.

By using the left mouse button select the following.

For position choose " type of fit" = "polynomial" and "order of fit" = "2" and "OK".

For the velocity select "type of fit" = "linear" and "OK".

For each graph the equation or average is displayed with the plots.

For position Ax˛ + Bx + C (A = ˝ a ; B = V_o ; C = X_o ; and x represents to t).

For velocity Ax + B (A = a; B = V_o ; and x corresponds to t).

These values should be compared to the corresponding values from your plots.

Record the data

With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button and drag the

table to top of window.

Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seen.

Record the time and the X-position of data in data table.

QUESTIONS:

1. State Newton’s second law.

2. What is the slope of the force Vs acceleration graph?

3. What assumptions were made in order to allow the calculation of the acceleration in this experiment?

4. If the mass of the car and the mass causing the acceleration were both doubled, how would the acceleration be changed?

DATA TABLE

D t = t_N - t_N-1 = is the same for all the above

Mass on horizontal m₁ = __________ Falling mass m₂ = __________

Acceleration from Newton’s second law. = __________

Acceleration from the slope of the velocity verses time graph. a = __________

% error in agreement with Newton’s second law % error = __________

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