INVESTIGATING NEWTON S SECOND LAW OF MOTION

Transcription

1 INVESTIGATING NEWTON S SECOND LAW OF MOTION Florida Sunshine State Standards Benchmark: SC.C The student explains and shows the ways in which a net force (i.e., the sum of all acting forces) can act on an object (e.g., speeding up an object traveling in the same direction as the net force, slowing down an object traveling in the direction opposite of the net force) Background Information: Airplanes fly. Joggers run. Skiers ski. These are all examples of motion. For an object to move, its position must change over time. The quantity that describes this change may be referred to as speed or velocity, depending on whether the direction of motion is significant. In essence, speed is a scalar quantity and depends only on the magnitude of the change in position over time, while velocity is a vector quantity and depends on both the magnitude and direction of the change in position over time. Ten meters is an example of scalar quantity; ten meters South or ten meters at sixty degrees North of South are examples of vector quantities. Other examples of scalar quantities include distance, time, and mass. Other examples of vector quantities include displacement, acceleration, and force. Graphical representation of motion includes graphs of position (d) versus time (t), velocity (v) versus time, and acceleration (a) versus time. Analysis of such graphs reveals relationships between the variables studied. Specifically, variables that are inversely proportional will produce a hyperbola. If one variable is directly proportional to the square of the other, a parabola will result. Variables that are directly proportional will produce a straight line. A line graph may be further analyzed by determining its slope, the ratio of the change in its dependent variable to the change in its independent variable. The slope of a displacement/time graph provides velocity while the slope of a velocity/time graph provides acceleration. Analysis of the area under a given graph also provides useful information. In fact, the area under a velocity/time graph yields displacement while the area under an acceleration/time graph yields velocity. Motion can not only be represented by graphs, but additionally, it can be described by Newton s three laws of motion. Basically, balanced forces result in constant velocity and unbalanced or net forces result in acceleration. This is why the velocity of a given object usually changes when it is subjected to forces such as gravity and friction. Neglecting air resistance, an object that is projected through the air will accelerate vertically due to the unbalanced force of gravity but will

2 maintain a constant horizontal velocity due to the absence of unbalanced forces. Thus, with the use of trigonometric functions, vertical and horizontal motion can be independently analyzed. When discussing motion, it is also important to consider the momentum or product of the mass and velocity of an object. According to Newton's Third Law of Motion, for every action there is an equal and opposite reaction. Therefore, in any closed and isolated system, momentum is conserved. This principle is of great significance when considering the flight of a rocket for as fuel is expelled downward, the rocket is propelled upward. There are many other topics within the realm of Physics, such as work and energy, which may be linked to motion. When examining all of these related topics together, one can better see a "big picture" relating Physics and Mathematics to the real world. This experiment is designed to verify Newton s 2 nd Law of Motion. Force equals mass multiplied by acceleration (F = ma). This law states that force on an object will cause it to accelerate in the direction of the force. The greater the force exerted on the object, the greater the acceleration. For any given force, the greater the mass of an object, the smaller the acceleration. In this experiment, the force will be applied by rolling balls of different masses down a ramp. A wooden, glass, and metal sphere will be used to vary the force used. A paper cup cut lengthwise will be used to measure the acceleration by measuring how far the box travels. The cup will be placed at the bottom of the ramp to catch the balls. A second part of this experiment will use a constant force (metal ball), and the mass of the object at rest (the cup) will be varied by adding washers to the top of the box. Timeframe: 90 minutes Materials Ramp at least 1 meter long; use cove molding or meter sticks with side rails on each side to keep the balls on the ramp) 3 balls (wooden, glass, and metal; 12 mm or ½ inch works well) Paper cup cut in half lengthwise 3 medium size washers

3 Meter stick / tape measure Graph paper 4 textbooks Tape Balance 10cm Meter stick Procedure: Part 1: 1. Read the entire procedure for both Part 1 and Part 2. Then answer the 1 st assessment question before starting the experiment. 2. Use a balance to record the mass of each of the spheres (wooden, glass, metal). 3. Make an inclined plane using the cove molding and four textbooks. 4. Place half a cup at the end of the ramp in such a way that it serves as a tunnel into which the sphere will roll to with the closed end of the cup facing away from the incline. 5. Measure 10 cm from the top of the ramp and draw a starting line, and labeling it 0 cm. 6. Measure the distance between this strip of tape and the bottom of the ramp. 7. Place a meter stick flat on the table/floor so that it extends from the bottom of the ramp. 8. Place the wooden sphere atop the ramp in such a way that the front of it is aligned with the strip of masking tape. 9. Record all data in a data table. 10. Release the wooden sphere and allow it to descend down the ramp. 11. Measure the length of time it takes for the wooden sphere to roll down the incline and the distance the cup moves. 12. Make observations concerning the descent of the sphere. 13. Record your data and repeat step 9-11 two more times for the wooden sphere. 14. Calculate the average time of descent. 15. Calculate the average speed during the descent. 16. Calculate the average distance by the cup moved. 17. Repeat steps 8 16 using the glass sphere (marble). 18. Repeat steps 8-16 using the metal sphere.

4 Part 2: 19. Tape one washer onto the outside of the cup. 20. Measure the cup's new mass. 21. Place the cup at the bottom of the ramp as before. 22. Repeat steps 8-16 with the metal sphere only. 23. Repeat steps with two and then with three washers.

5 DATA TABLE Sphere Mass of Cup & Washers Mass of Sphere (g) Ramp Length (cm) Time (s) Trials Average Time (s) Average Speed (cm/s) Distance Traveled by Cup (cm) Trials Average Distance Traveled by Cup (cm) Wooden Glass Metal 1 metal washer 2 metal washer 3 metal washer Analysis Questions: 1. Write a hypothesis for both parts of this experiment. Part 1 Part 2 2. How does the mass of the moving object (mass of sphere) affect the speed of the sphere? 3. How does the force of the moving object (type of sphere) affect the distance traveled by the cup? 4. How does the mass of the object at rest (cup without/with washers) affect how far it travels when hit by each of the different spheres? 5. Describe the relationship between force (mass of ball) and the distance the cup moved. 6. Describe the relationship between the mass of the box or cup and the distance the box or cup moved.

6 7. Construct a bar graph of the mass of the sphere (x-axis) versus the average time it took for each of the spheres to roll down the ramp (y-axis). 8. Draw conclusions. 9. Construct a graph of the mass of the sphere (x-axis) versus the average distance traveled by the paper cup without washers (y-axis) for the three different spheres that were used. 10. Draw conclusions. 11. Construct a graph of the mass of the paper cup (x-axis) versus the average distance traveled by the paper cup (y-axis) for the metal sphere. 12. Draw conclusions. 13. Do you agree with Newton s 2 nd Law of Motion? 14. Did your results support your hypothesis? Explain.

7 Assessment: Student grades will be based upon completion of the activity, the analysis questions, and the graphs. Use a rubric such as one found in the appendix to assist in the scoring. Home Learning: Students will complete the analysis questions and the graphs. Extensions: 1. Use a CBL motion system to record motion and determine speed with greater accuracy. 2. Use a CBL accelerometer system to record motion and determine acceleration. 3. Mark the ramp at 25 cm intervals and record the time(s) as it passes each mark. These additional readings will allow students to compute acceleration of the spheres. v 1 v 2 a = t 1 - t 2 4. Investigate what happens to speed and force when friction is introduced as a variable. Line the ramp/track with different materials, e.g., wax paper, sandpaper, cloth, carpet.