Lab 105 - NEWTON'S SECOND LAW OF MOTION OBJECTIVE To gain confidence that Newton's Second Law of Motion is valid. BACKGROUND In class, we did a quick demonstration that suggested that the acceleration of an object is proportional to the force acting on it and inversely proportional to the object's mass. This relationship, usually rewritten as En F. = ma, is known as the Second Law of Motion. You will apply a number of known forces to a mass and measure the corresponding accelerations, then generate a graph that will help convince you of the validity of the Second Law (see Figure 1). The accelerating force will be the weight of the hanging mass, gm.' The mass being accelerated is the mass of the glider with all of its parts, plus the hanging mass. In order to change the accelerating force, mass must be moved from the glider to the hanger so that the total mass being accelerated remains constant. PROCEDURE Small masses Place the air-track on the table such that the hose end is towards the wall and the Hook plug- -Balancing plug free end is about ten cm over the edge wheel Air track of the table. Attach the Smart Wheel to the end of the track; it should fit into the hollow end of the track. Do not clamp it to the table. Make the table as level as possible. Place the glider on the track, I Hanging make run the thread (~1 m long) over the end of the track and over the wheel, down to Figure 1 - Apparatus for testing the Second Law of Motion. the hanging mass holder. Adjust the system so that the string is as horizontal as possible and runs directly over the wheel; in this way, there are no force components that are not directly along the length of the track to worry about. Strictly speaking, we made use of the Second Law to conclude that the gravitation force on an object is gm, so our logic is somewhat circular. However, remember our discussion that nothing can really be proven in Physics; we want to show that our experimental results are consistent with the Second Law. 37 2. Attach the cable from the Smart Wheel to DIGITAL INPUT ONE on the Pasco box. The Smart Wheel has an infrared photo-gate that tells the computer when the beam is blocked by one of the spokes, and when it is not. Knowing the circumference of the wheel (0.191m) and the number of degrees between each spoke on the wheel (36) allows the computer to calculate the velocity of the mass, assuming that the string does not slip on the wheel, of course. Tum on the Pasco box and the computer. When the desktop appears, double click on the Newton_//.cap icon. This worksheet should already contain the parameters you will need for the experiment. 3. Mass the glider, the hanger, and all of the small masses (two 5g and two 10g masses) together as one object to find the total mass that is being accelerated, ' M. Half of the groups should also include the two 50g masses, while the other half will not.? Find the mass of the hanger, m. Remember that the masses on the glider must always be balanced front-to-back and side-to-side 4. Place the glider on the track with the small 5g and 10g masses on the glider's pins, run the string over the wheel, and place the mass hanger only on the lower end of the string. What is the force being applied by gravity to the hanger? Calculate it in newtons. Turn on the air and release the glider. The instant after the glider is released, hit the RECORD button in CAPSTONE. Try to press STOP before the hanger reaches the floor, if possible. If not, you can fix this later by deleting points from the graph. 5. Examine the graph of the velocity data you have taken. If you have done everything correctly, you will observe a straight positive slope line. If so, continue to Step 6. More likely, though you will probably observe a curve resembling the letter lambda: 'A.' If so, you continued to take data past the time at which the hanger hit the floor. This is easy to fix. Click the button labelled HIGHLIGHT RANGE OF POINTS IN ACTIVE DATA. A box should appear. Move the box over the data points on the graph you wish to delete. Right click the box and choose DELETIONS - DELETE HIGHLIGHTED DATA POINTS; the unwanted data should disappear. You may need to perform this process for data points at the beginning of your run as well. 6. Once you have a straight line of velocity v. time, you will need to perform a linear fit, the slope of which will be equal to the acceleration of the mass. Click the APPLY SELECTED CURVE FITS TO ACTIVE DATA button and, if necessary, choose LINEAR. The equation of the fit should appear on the graph. Record the acceleration, a, in meters/second?. 7. Move 10 grams total from the glider to the hanger (i.e. move the two 5g masses) and repeat Steps 4 through 6. Continue by adding another 10 grams (by returning the 5g masses to the Underlined quantities are to be recorded on your worksheet. If you are in an honors class, you will do both with and without the extra mass. 38 glider and putting the 10g masses on the hanger) and repeat Steps 4 through 6. Lastly, add 10 grams more to the hanger by moving all of the small masses to the hanger. Repeat Steps 4 through 6. NEVER move the large masses to the hanger. HONORS EXERCISE: Repeat Steps 3 through 7, except this time, include (or don't Include) the two 50g masses as part of the glider. ANALYSIS 1. In this exercise, what was the independent variable and what was the dependent variable? 2. Consider the proposed relationship between applied force and the resulting acceleration. How will you plot your data? Do so, now. 3. What specific shape does your curve possess? What physical quantity does the slope of your curve represent? Determine the value of that quantity from the slope and compare your value to the measured value found directly earlier. Do a percent difference4. What is the value of your intercept? What does this value say about the relationship between the applied force and the acceleration? 5. In a formal report, address the following in the Results section: a) Describe the data collected and present the graph. b) Explain how the mass of the system was found from the slope of the graph c) State the value you found experimentally and the accepted value, and perform a per cent difference calculation. HONORS EXERCISE: Repeat the analysis for the second set of data. CONCLUSION - Consider these questions as you write your conclusion. 1. What type of relationship exists between the force and the acceleration? How is this indicated on your graph? 2. What is the constant of proportionality, and how close is it to the expected value? HONORS EXERCISE. Show more directly (than in Part 1) that the acceleration is inversely proportional to the mass of the object for a given force. Replot your data to show this. 39 Note that you will have four lines with two points each rather than two lines with four points each. Does each line show the correct relationship? Comment on the expected values of the slopes of these lines, and compare with the values obtained in the experiment. 40 WORKSHEET for Lab 105 - NEWTON'S SECOND LAW OF MOTION You MUST turn in a written, formal report for this exercise. OBJECTIVE: Mass M (w/o 50g masses) = Mass M (w/ 50g masses)= Hanging | Accelerating Acceleration Hanging Accelerating Acceleration Mass Force Mass Force (kg) (gmH (m/s?) (kg) (=gmH) (m/s?) (Newtons) (Newtons) Slope of best-fit line = Slope of best-fit line = Mass M as determined from the graph = Mass M as determined from the graph = y-intercept = y-intercept= Per cent difference = Per cent difference = CONCLUSION