The Second Law of Motion

Transcription

1 The Second Law of Motion Theory: The Second Law of Motion states that: The acceleration of an object is directly proportional to the net force applied to the object and inversely proportional to the mass of the object. If the acceleration is in units of meters/sec 2, the mass is in units of kilograms, and the force is in units of Newton s, then the second law of motion is expressed by the equation F = ma [1] In equation [1], F is the net applied force, m is the mass of the object on which the force is applied, and a is the acceleration of the object in response to the force. In this experiment, a force will be applied to a cart of mass m 1 (mass of cart plus the added mass), by hanging weights on a string which is attached over an almost frictionless pulley to the cart, as sketched in Figure 2-1. There is however, some friction between the cart and the track. Let F f be the force of friction which opposes the motion of the cart. The hanging weight W 2 is opposed by the force of friction on the cart, F f. Recall that the weight, W 2, is related to the mass, m 2, by the equation m1 W 2 = m 2 * g, [2] smart pulley Leveling Knob Stop m2 Figure 4-1

2 Procedure: where g is the acceleration due to gravity (about 9.8 m/s 2 ). The net force, which accelerates both the cart and the hanging mass (i.e., the total mass of the system), is then F = ( W 2 - F f ), Hence, equation 1 may be rewritten as W 2 - F f = ma [3] W 2 = ma + F f [4] where m is the total mass of the system, i.e. m = m 1 + m 2. Notice that Equation [4] is of the form of a straight line, y = kx + b, provided the total mass (m 1 + m 2 ) is constant as W 2 is varied. Thus, theory predicts that if the hanging weight is plotted as a function of the acceleration of the system, a straight line should result. To find the acceleration of the system a computer is used in this experiment. Using the Data Studio program, and a measurement device called the Smart Pulley; the velocity of the cart will be measured as a function of time. This data is plotted in a Graph Window and the slope of the resulting straight line will be the acceleration of the system. Initial Setup: 1. Turn on the computer. Select the Lab User account. Open the Data Studio Program. Once the program has loaded, select Open Activity, and within the 1401 folder open the file Newton s 2 nd law. 2. Assure that the smart pulley is plugged into Digital Channel 1 input. 3. Pull the strap within the catcher mechanism so that it is straight across the track. Place the cart so that the end with the string is touching the strap of the catcher mechanism, as shown in Fig Guide the string over the pulley attach the 50gm hanger to the loop at the end of the string. An slowly lower the hanger to the floor. Adjust the catcher mechanism so that the hanger just touches the floor. Place the foam pad under the hanger. There is no need to readjust as this is only to provide padding to prevent damage to the hanger when it strikes the floor. 4. Remove the hanger and center the cart on the track. Gently nudge the cart with a finger in one direction. The cart should only move a small distance and then stop; if it continues to roll down the track then it is necessary to level the track. Adjust the leveling knob that is on the opposite end of the track from the smart pulley. Place the cart in the center of the track again and repeat, until you are certain that the track is level. Be sure to nudge the cart in both directions.

3 Test Run: 5. Start out by making a practice run using only the cart and the 50 gram hanger. Attach the hanger to the free end of the string. The string should pass over the pulley and the hanger is suspend above the floor. Adjust the strap on the catcher so that it spans across the track. The catcher is used to bring the cart to a gentle halt. Move the cart approximately 60 cm away from the catcher (Not to the 60cm location on the track) and hold it there. A lab partner should then select the Start button on the Experiment ToolBar, once selected and it name changes to Stop the lab partner holding the cart should release the cart. After the cart has completed its run down the track, Select Stop. It is OK if additional data collects after the cart is caught. As long as there is a linear line showing the carts acceleration down the track, there should be enough data to complete the analysis of the data run. 6. The acquired data displayed in the graph window represents equation 5. The slope of the graph will yield the acceleration of the cart. v = v o + at [5] 7. Activate the Graph Window by clicking on the Graph TitleBar. On the Graph ToolBar there are a series of buttons. The first button is the scale to fit button. Select this button to obtain the best display for the data. The area of interest is the initial sloped straight line. Position the mouse pointer just above one of the data points near the top of the line. Click and drag the mouse pointer to select data points along this line. Release the mouse button, the data along the sloped line will be highlighted. On the Graph ToolBar select the Fit button and from its ensuing popup menu select Linear Fit. A heavier line should now be seen and if the data is properly selected it falls on top of the data line and a box appears that display information for the linear fit of y = mx + b. The value of the slope, m, is the acceleration of the cart. Data Collection: 8. Start as you did in the test run, but with the falling mass set to 0.2 kg (remember the weight hanger is 0.05 kg) and then place the remaining 0.4 kg onto the cart. Acquire a data run with the 0.2 kg falling mass. Record the acceleration value in Data Table 1 Calculate the force supplied by the falling mass to the cart. W 2 = falling mass * gravity. In the first case 0.2kg * 9.8m/s 2 = 1.96 N Note: It is essential that the total mass of the system is constant. The mass on the cart and the falling mass should always total 0.60 kg. Therefore, when W 2 is increased mass is moved from the cart to the hanger. The 50 gram mass will be moving from the hanger to the cart and vice versa as W 2 is increased. 9. Repeat step 8 for each falling mass in Data Table 1.

4 Data Page Data Run n hanging mass (kg) Data Table 1 a (m/s 2 ) W 2 (N) Plot W 2 vs. a and determine the slope and y-intercept and record the information below. m graph = ( ) b graph = ( ) Questions Is the statement for the Second Law of Motion The acceleration of an object is directly proportional to the net force applied to the object valid for this experiment? Explain. The total mass of the system is represented by the slope of the line you just plotted. With the knowledge of the total mass of the system: Determine the mass of the cart. Determined mass of your cart? ( ) Compare this with the mass of the cart measured with a triple beam balance.(the string should be regarded as part of the mass even though it is nearly massless.) Measured mass of your cart? ( )

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