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Physics 211: Newton’s Second Law Sir Isaac Newton Born: January 4, 1643 Died: March 31, 1727 Reading Assignment: Chapter 5, Sections 5-9 Chapter 6, Section 2-3 Portrait of Isaac Newton by Sir Godfrey Kneller http://www.newton.cam.ac.uk/art/portrait.html Introduction: Kinematics is the study of how objects move. Dynamics, on the other hand, focuses upon why objects move. Our own human experience tells us that forces have something to do with causing motion. Aristotle developed a theory of motion based completely upon human experience and reason. He stated simply that all motion, even constant velocity, was caused by the existence of forces. Objects at rest, according to Aristotle, had no forces acting upon them. Spontaneous motion, such as letting go of a rock and watching it magically pick up speed as it fell to the earth, was explained by the fact that all objects had a natural place in the universe. A rock’s natural place was on the ground. Therefore, when a person released a rock from their grasp, it automatically returned to its natural place. The force arose from the object being out of its’ “natural” place and wanting to return to its “natural” place. Aristotle, however, never actually verified his theory with experimentation. If he had, he would have found flaws in his thinking. Many people today still hold Aristotelian views. However, Newtonian theory takes a very different stance. The power of Newton’s theories was revealed through their ability to make detailed mathematical predictions about the motion of objects. These predictions have consistently been verified experimentally. Newton hypothesized that forces cause a change in motion, not motion itself. In addition, he carefully distinguished between individual forces and the net force acting on an object. He said that if the Net Force acting on an object was zero, then the object would continue to move with constant velocity. Constant velocity includes two important parts: constant magnitude (speed) and constant direction. [Note: 1) An object at rest is a special case of the speed being equal to zero; 2) A frame of reference is needed to define each of these parts.] In a sense, Newton felt that moving at constant velocity was an object’s “natural place in the universe.” Newton also carefully explained what would happen to an object that experienced a Net Force with a magnitude of something other than zero. Fnet ma © 2004 Penn State University Physics 211R: Lab – Newton’s Second Law This version of Newton’s Second Law is popular because it clearly demonstrates the relationship between Net Force and Acceleration. After studying kinematics, acceleration is a quantity with which many students are familiar and comfortable. Similarly, most people are familiar with the concept of Force, but many do not have a realistic number sense of its magnitude expressed in newtons. For example, what is the magnitude of the force provided by a Saturn V rocket (i.e. Thrust)? How does the force on a basketball differ from the force on a bullet when each is “shot?” Many people are not aware that a bullet and a basketball each experience approximately the same change in momentum. Why would this be? As you perform this lab, make some mental notes regarding the size of the values that you calculate for your answers. It is essential that you develop a good sense of what is realistic. © 2004 Penn State University Physics 211R: Lab – Newton’s Second Law Newton’s Second Law Goals: Verify that a constant net force causes a constant acceleration by collecting data, graphing each vs. time, and analyzing the data during the appropriate time interval. Determine the mass of an unknown object by graphing Net Force vs. Acceleration. Equipment List: Low Friction Track with cart Ultrasonic motion detector force probe pulley system Science Workshop Excel™ scale balance hanging masses 灺 Shown at left is NASA’s Saturn V rocket as it blasts off on July 16th, 1969 with the crew of Apollo 11 sitting on top. The Saturn V rocket was the largest rocket ever used by NASA, and the only one able to lift the large masses needed to land astronauts on the moon. Photo courtesy of NASA Lab Activity 1: Determine the Mass of an Unknown Cart What is the mass of the cart (including the force probe) sitting on the track at your lab station? One way to measure mass is to use a scale balance. However, this method will not be available to you until the end of the lab. Therefore, you must find it indirectly using another method. Newton’s 2nd Law states: “if a net force acts upon an object, then the object will respond by accelerating in the direction of the net force.” In addition, a constant net force should result in a constant acceleration. Fnet ma © 2004 Penn State University Physics 211R: Lab – Newton’s Second Law This method uses the motion detector and force probe to measure the acceleration and net force, respectively, acting on the cart. The net force is caused by a mass that is hanging over a pulley at the edge of the track. Gravity ensures that this force will be constant. Once this data is taken, the mass can easily be calculated. It is important to note, however, that all good experiments rely upon more than one data point. Therefore, you will repeat this experiment for different accelerations and corresponding net forces while keeping the mass (the cart) the same. All of the data will be graphed together to determine the mass. 1. Set up Science Workshop to read the data collected by the motion detector and force probe. Create graph windows of Position, Velocity, Acceleration, and (Net) Force vs. Time so that the data will be displayed on the screen as each run is taken. The motion detector does not need to be calibrated. However, the force sensor must be rezeroed often throughout the lab. In order to do this, first remove all tension from the force sensor. Then, press the TARE button to reset the force sensor to zero1. Repeat this procedure before each trial. 2. Place a hanging mass at the end of the string. (Suggestion: 20g, 40g, 60g, …) 3. Release the mass and record your data. 4. Using the graphs that you created on Science Workshop, notice the time interval during which the cart was being freely pulled by the hanging mass. (The force and acceleration data should be relatively constant.) Click and drag to highlight this region on each graph. (Note: the graphs can be resized and enlarged.) 5. Using the icon on Science Workshop, perform statistics calculations on this region of the data for this trial. Calculate: (1) the Acceleration and (2) the Net Force. Hint#1: the constant net force is the mean y-value of this region of data on the force vs. time graph. 1 Calibration of the Force Probe See the previous lab (Newton’s First Law) for instructions on how to calibrate the force sensors. © 2004 Penn State University Physics 211R: Lab – Newton’s Second Law Hint#2: the constant acceleration is either the mean y-value of this region of data on the acceleration vs. time graph or the slope of this region of data on the velocity vs. time graph. 6. Open Excel™. Create a table in which to place the Acceleration and Net Force data point that you determined in step 5. Place these values in your table as one data point. 7. Repeat steps 2-6 for at least 6 different hanging masses. (Note: This will provide a set of 6 data points from which the mass can be determined.) Import the Excel™ Acceleration and Net Force Table containing all of your collected data into the Template. 8. Construct a Net Force vs. Acceleration graph in Excel™. (Import this graph into the Template.) What does the slope of this graph represent? Find the value of the slope (including units). Does your graph pass through the origin? If not, explain why it doesn't. 9. Measure the actual mass of the cart (including the force probe) using the scale provided by your TA. 10. Calculate the % error between the calculated and actual values for the mass of your cart. (By what percentage does your calculated mass differ from the mass measured on the scale?) Comment on the result by including a discussion of error in your answer. (Hint: You may wish to complete Activity 2 before completing this question.) Lab Activity 2: Free Body Diagrams 1. Draw a force diagram of the cart as it is being pulled across the level track. If the Net Force does not equal zero, then also indicate the direction of the Net Force on the cart. 2. Draw a force diagram of the hanging mass as it is allowed to fall freely, pulling the cart. If the Net Force does not equal zero, then also indicate the direction of the Net Force acting on the hanging mass. 3. What force does the force probe actually measure? (In Activity 1, it is stated at measuring the Net Force. Is this true? Under what conditions?) 4. Compare the value of the Net Force (measured by the force probe) in each of your 6 trials in Activity 1 to the actual weight of the hanging mass. Are they equal? If not, which one is greater and why? © 2004 Penn State University Physics 211R: Lab – Newton’s Second Law