Newton s Second Law. Part I

Transcription

1 Newton s Second. Part I Reading Assignment: Chapter 5, Sections 2-4 Chapter 6, Section 4 Photo by Keith Larrett Introduction: A common misconception is that astronauts are not subject to the force of gravity during space flight. In reality, for missions orbiting the earth, astronauts are subject to a force of gravity that is only slightly less than what they would experience on the earth s surface. Why, then, do they appear to be weightless? The answer is simple. While in orbit around the earth, they experience free fall motion in the same way that skydivers do. (There is simply no air pushing against them.) Free fall motion provides the sensation called weightlessness. Both orbiting astronauts and skydivers undergo free fall motion. There is a difference, however. The difference between skydivers and astronauts can be illustrated by looking at the forces acting upon them. An astronaut orbiting the earth is subject to only one force, the force of gravitational attraction to the earth. A skydiver, on the other hand, is subject to two forces: gravitational attraction to the earth and air resistance. Different net forces cause different types of motion. Since an astronaut is subject to only one force, the net force cannot be equal to zero. Newton s Second states that this type of situation causes accelerated motion. In this case, the astronaut is accelerating towards the center of the earth with centripetal acceleration. The result is circular, or orbital, motion. Because a skydiver is subject to two forces, the net force may or may not be zero. The value of the net force depends upon the magnitude and direction of each of these forces. Newton s Second, the of Inertia, states that (in an inertial reference frame) a net force of zero causes an object to be at rest or in motion with constant velocity. The purpose of this lab activity is to investigate each of these cases. Air resistance is not a constant force. As you fall through air (or water or oil) a viscous force, air resistance, is generated as you push the molecules out of the way. This force increases with your velocity, the density of the medium and your cross-sectional area. A skydiver, after jumping out of a plane, eventually comes to be in equilibrium when air resistance balances the force of gravity pulling downwards. At this point, the net force is zero and the velocity becomes constant. This constant velocity is known as terminal velocity. Since our insurance was cancelled after the last class "jump," you will explore this phenomenon using coffee filters. What does it mean for the Net Force on an object to equal zero? Many students think that it means there are no forces acting on the object. This is incorrect. The term Net Force is used to symbolize the sum of all of the individual forces. r n r F net = F i i= 1

2 Since force is a vector quantity, both magnitude and direction must be considered when forces are added. Equilibrium results when these forces effectively cancel each other out. In other words: F r net = 0 What happens to the motion of an object if the Net Force on it equals zero? Many students think that the object must be at rest, but this is only true if the object was at rest originally. If the object was in motion originally, then the object remains at constant speed in one direction for as long as the forces are in equilibrium. Newton s Second of Motion, although simple to describe, is not intuitive. Understanding it and applying it to different situations can be difficult. Remember that Newton s s are the foundation of dynamics, the study of why objects move the way that they do. Relationships between force and motion are one of the central themes of Mechanics.

3 Newton s Second Goals: Verify that Newton s Second applies to objects at rest. Verify that air resistance causes an object to reach a state of equilibrium. Investigate the relationship between air resistance and velocity. Equipment List: Force table w/ Force sensor & 3 pulleys Data Studio Excel Hanging masses Motion Detector Coffee Filters Scale Balance Calibration of the Force Probe Lab Activity 1: Newton s Second for an Object at Rest Prior to beginning this activity it will be necessary to calibrate the force sensor. This can be accomplished in just a few easy steps once the force probe has been installed in Data Studio. First click on the Setup button to bring up the Experiment Setup window. Scroll down the list and choose Force Sensor. Once the force sensor has been selected double-click the force probe icon to open the sensor properties window. Next, click on the Calibration tab. There are three boxes that we will want to look at in this window. Remove all masses from hanging on the force sensor and push the TARE button on the side of the force probe. Enter 0 (zero) in the Low Point window and press the Take Reading button below. Next, hang a known mass, and hence a known weight, from the force sensor. (If you re working on a force table you can hang the known mass directly opposite to the sensor.) Record the weight of the mass in the High Point window and press the Take Reading button directly below. Finally, make sure that the Low Sensitivity (1x) window is selected in the drop down menu. This may be the only time that you may need to calibrate the force sensor during this lab. However, as the lab progresses you will need to periodically re-zero the probe by pushing the TARE button on the side of the probe. 1. Set up Data Studio to read the data collected by the force probe located on the force table. While nothing is pulling on the force sensor, press the TARE button to zero it. Do not graph the data. Instead, set up a Digits screen. 2. Place three different masses on the other strings. Move the pulleys around the force table until the ring is held in equilibrium over the very center of the table. 3. Make a sketch of your force table. Label each mass and record the angle positions of each of the strings. 4. Calculate the magnitude of the force (in Newtons) exerted on the ring by each of the hanging masses. Be sure to include the mass of the hook. Add this information to your sketch.

4 5. Determine the magnitude and direction of the resultant of the three force vectors created by the hanging masses. Clearly explain your method of vector addition. 6. Compare your resultant to the force exerted on the ring by the force probe. What do you notice? 7. Is it reasonable to conclude that Newton s Second has been verified for an object (the ring) at rest? Explain. Lab Activity 2: Newton s Second for an Object Moving with Constant Velocity 1. Set up Data Studio to read the data collected by the ultrasonic motion detector. Create graphs of Position vs. Time and Velocity vs. Time so that the data will be displayed on the screen as it is obtained. 2. Place the motion detector carefully on the floor, facing upward. Choose the wide beam mode. Practice holding a coffee-filter high above the detector so that, when released from rest, it falls and rests upon the detector (or close to it). 3. Record the motion of the falling coffee-filter. Be sure to obtain a set of data in which the sensor picked up the entire motion of the filter, starting prior to its release. Was terminal velocity (equilibrium) reached? How can you tell? How much time did it take the filter to reach terminal velocity? Import the graphs of one trial to your template. 4. Determine the value of the terminal velocity of the coffee-filter. Explain how you did this. 5. Measure and record the mass of your coffee-filter using a scale provided to you by your instructor. 6. Draw a free-body (force) diagram of the coffee-filter while it was experiencing terminal velocity. 7. Use Newton s Second to determine the magnitude of the force of air resistance acting on the coffee-filter while it was experiencing terminal velocity.

5 Lab Activity 3: The Nature of Air Resistance 1. Consider the coffee-filter data obtained between the time that it was released and the time that it reached terminal velocity. What evidence is there of acceleration? Does the data suggest that the acceleration of the filter is constant, increasing, or decreasing? Explain. 2. Draw a free-body (force) diagram for the filter for each of the following: 1) the moment of release from rest; 2) before reaching terminal velocity; 3) after obtaining terminal velocity. In your sketches estimate the magnitude of the various forces at each of the times. 3. According to theory, what is causing the force of air resistance on the coffee-filter to change? Is the magnitude of the force of air resistance increasing or decreasing during this time interval (from the moment of release until the terminal velocity has been reached)? Why? 4. Describe how the magnitude and direction of the Net Force on the coffee-filter is changing over this time period (from the moment of release until the terminal velocity has been reached). 5. Explain why it is inappropriate to apply Newton s Second to the coffee-filter during this time period. Activity 4: The Relationship between Air Resistance and Velocity 1. Repeat the data taking procedure used in Activity 2 for at least 6 different masses of coffee-filters. (Different masses of coffee-filters can be obtained by stacking filters together.) After each run, calculate the value of the terminal velocity and the force of air resistance acting on the filter while experiencing terminal velocity..