1. What does the catapult exert on or apply to the plane?

Transcription

1 Unit 1: Forces and Motion Lesson 2.b Newton s Second Law of Motion Newton s laws predict the motion of most objects. As a basis for understanding this concept: Students know how to apply the law F = ma to solve one-dimensional motion problems that involve constant forces (Newton s second law). Student Performance Outcomes Students will determine the acceleration of an object in an Atwood s and Modified Atwood s machine. Students will determine the net force exerted on an object in an Atwood s and Modified Atwood s machine. Students will graph and interpret the relationship between net force, mass and acceleration. DO NOT WRITE ON THIS HANDOUT Engage On an aircraft carrier, aircraft are attached to catapults, which give them the necessary acceleration to go from a standing position to 165 miles per hour (265.5 km/h) in just two seconds. 1. What does the catapult exert on or apply to the plane? 2. Prepare a free body diagram for a plane accelerated by an aircraft carrier catapult. 3. Sketch the appearance of a position vs. time, velocity vs. time and acceleration vs. time graph for the jet (assume uniform acceleration). 4. If the mass of the plane were to be increased (ex. extra fuel tanks attached to wings), what affect do you think this would have on the acceleration of the plane? 5. If the catapult were to be given extra steam (increasing the force it exerts on the plane), what affect do you think this would have on the acceleration of the plane? 1

2 Explore Consider this situation. The motion sensor and computer can provide us specific information about the acceleration of the system consisting of 2 masses connected by a string. We will use this information to develop a graph of force vs. acceleration. The shape of this graph will tell us about the relationship between force and acceleration. ü Go to the website indicated above. If the link is active it will take you directly there by clicking on it or you have to type it in. ü For starting mass on the left choose 105 g and on the right 95 g ü The combined mass of the two individual masses will always have to be 200g. ü After hitting the start use the velocity-time graph to calculate the acceleration of the system. The steepness or slope of this graph represents the acceleration. You have to calculate the slope of the line of best fit. ü slope = y 2 - y 1 x 2 - x 1 = ü ü Record the masses and accelerations in a table like the one below. Make sure you conduct 2 trials. Yes, we know that this is a video program, but it helps us make sure we didn t make a mistake in our calculations. Mass of left hanger (kg) Mass of right hanger (kg) Gravity on left hanger: Mass times 9.8 m/s 2 (N) Gravity on right hanger: Mass times 9.8 m/s 2 (N) Net force = Gravity on left hanger minus gravity on right hanger (N) Acceleration (slope from velocity-time graph) (m/s 2 ) Trial 1 Acceleration (slope from velocity-time graph) (m/s 2 ) Trial 2 Average Acceleration of the system (m/s 2 )

3 Plot Acceleration (x axis) vs. Force (y axis) on the grid below. It is important to note that the hanging masses are part of an accelerated system. When one part of this system moves with a given acceleration the entire system moves with that acceleration. 6. What is the mass of the system? 7. Create a graph of Net force (measured in Newton, the unit of Force) versus Acceleration (m/s 2 ). Use our graphing basics when creating this graph. 8. Draw a best-fit line that follows the trend of the resulting points on your graph. 9. Is the relationship between force (weight) and acceleration linear? 10. Describe the relationship between the force and the acceleration of the system. Is it directly proportional (as one variable increases so does the other) or is it inversely proportion? Explain how you know. 11. Select two non-data points from the resulting best-fit line on your graph. Write these below in coordinate form (x 1, y 1 ), (x 2, y 2 ). 12. Calculate the slope of your best-fit line by using the two non-data points that you selected in number 11. Be sure to carry through with your units and to label your answer with the appropriate units. slope = y 2 - y 1 x 2 - x 1 = 13. What does the slope of your best-fit line correspond to? Where else did you see this number? 3

4 14. Why did the total mass of the system have to stay the same at 200g or 0.2kg? 15. If the force increases, what happens to the acceleration of the system? Explain 16. Three students in your class have different ideas about the magnitude of forces and changes in velocity. Carefully read the student arguments and decide which statement is best supported by the evidence. Student A The size of an unbalanced force has no affect on the amount of acceleration experienced by an object. All that matters is that the force is unbalanced. If there is an unbalanced force, the object will experience acceleration. Student B The bigger the pull or the push, the bigger the change in motion experienced by an object. There is a linear relationship between the size of the exerted force and the acceleration experienced by an object. Student C The amount of mass to be moved is also important. If the mass is increased and the force is kept steady, then the acceleration will decrease. Isaac Newton was the first to recognize that the acceleration of an object is directly proportional to the net force exerted on an object. This linear relationship, Newton s Second Law of Motion, is defined in the following way: F net = m a Another way of stating this law is that the acceleration of an object is directly proportional to the net force exerted on it. A biography of Newton can be found at: or you can simply google Isaac Newton Biography. Write down 5 facts about Newton that you thought are interesting or surprised you. 4

5 Elaborate Design an experiment that would allow you to find the mass of a heavy crate, too heavy to put on a scale. You only have a spring scale, a motion sensor and a low friction rolling flatbed available. Make sure to give enough detail to allow another student to perform the experiment exactly as you intended. 5

6 Evaluate I Consider the set up illustrated below. The nuts have identical masses and the pulley is frictionless. The paperclip has a small, but significant mass. 25. If you were to release nut B, what kind of motion do you predict nut A would have? 26. Sketch the motion graphs that you would expect for nut A after releasing the system. 23. Draw a free-body diagram for nut A. 24. Draw a free body diagram for nut B that includes the paper clip. 27. If you were to release nut B, what kind of motion do you predict nut B would have? 28. Sketch the motion graphs that you would expect for nut B after releasing the system. 6

7 Evaluate II 29. Summarize Newton s Second Law. (Don t simply say that F=ma) Answer the following questions. Include an explanation for your choices. 30. This is a frictionless system. Select the best fee-body diagram for this situation. a) b) c) d) e) 31. This is a frictionless system. What would an x vs.t graph look like for this system? a) c) e) 32. This is a frictionless system. Determine the acceleration rate for the block. b) d) a) 0.5 m/s b) 0.5m/s 2 c) 2.0 m/s d) 2.0m/s Select the best a free-body diagram for this situation. a) b) c) d) e) 34. What would an x vs.t graph look like for this system? a) c) e) 35. Determine the acceleration rate for the block. b) d) a) 0.5 m/s b) 0.5m/s 2 c) 2.0 m/s d) 2.0m/s 2 7