Lab 4 - Force and Motion

Transcription

1 Lab 4 Force and Motion L4-1 Lab 4 - Force & Motion L04-1 Name Date Partners Name Date Partners Lab 4 - Force and Motion LAB 4 - FORCE AND MOTION A vulgar Mechanik can practice what he has been taught or seen done, but if he is in an Aerror vulgar he knows Mechanik not how can to practice find it out what and correct he hasit, been and taught if you put or him seenout done, of his but if road, he is in he an is at error a stand; he knows whereas nothe how that tois find able it to outreason and correct nimbly it, and and judiciously if you put about figure, force and motion, is never at rest til he gets over every rub. him out of his road, he is at a stand; whereas he that is able to reason nimbly and Isaac Newton judiciously about figure, force and motion, is never at rest til he gets over every rub. OBJECTIVES To learn how to use a force probe to measure force. Isaac Newton To understand the relationship between the direction of the force applied to an OBJECTIVES object and the direction of the acceleration of the object. To explore Newton s first and second laws of motion for one-dimensional motion To (along learna how straight to useline) a force probe to measure force. OVERVIEW To understand the relationship between the direction of the force applied to an object and the direction of the acceleration of the object. In the previous labs, you have used a motion detector to display position time, velocity time, To exploreand Newton s acceleration time first and second graphs laws of motion of different for one-dimensional motions of various motion (along objects. a You were straight not line) concerned about how you got the objects to move, that is, what forces ( pushes or pulls ) acted on the objects. OVERVIEW From your own experiences, you know that force and motion are related in some way. To start In the your previous bicycle labs, moving, you have you used must a motion apply detector a force to to display the pedal. position time, To start up velocity time, your car, you and acceleration time graphs of different motions of various objects. You were not concerned must step on the accelerator to get the engine to apply a force to the road through the about how you got the objects to move, that is, what forces ( pushes or pulls ) acted on the tires. objects. But exactly how is force related to the quantities you used in the previous lab to describe From your own experiences, you know that force and motion are related in some way. To start motion position, velocity, and acceleration? In this lab you will pay attention to forces your bicycle moving, you must apply a force to the pedal. To start up your car, you must step on and the how accelerator they affect to get motion. the engine You to apply will a first force develop to the road an idea through of a the force tires. as a push or a pull. You will learn how to measure forces. By applying forces to a cart and observing the nature But exactly of its how resulting is force related motion to the graphically quantities with you used a motion in the previous detector, lab toyou describe will motion come to understand position, velocity, the effects and of acceleration? forces motion. In this lab you will pay attention to forces and how they affect motion. You will first develop an idea of a force as a push or a pull. You will learn how Another to measure major forces. goal By of applying this lab is forces to continue to a cart to andexplore observing the the relationship nature of its between resultingforce motion and acceleration: graphically with the first a motion two detector, of Newton s you will famous comelaws to understand of motion. the effects of forces on motion. Another major goal of this lab is to continue to explore the relationship between force and University acceleration: of Virginia the first Physics two of Department Newton s famous lawsmodified of motion. from P. Laws, D. Sokoloff, R. Thornton PHYS 1429, Spring 2011

2 L4-2 Lab 4 Force and Motion INVESTIGATION 1: Motion and Force You can use the force probe to apply known forces to an object. You can also use the motion detector, as in the previous two labs, to examine the motion of the object. In this way you will be able to explore the relationship between motion and force. You will need the following additional materials: L04-2 motion detector Lab 4 - Force & Motion rectangular brass piece INVESTIGATION 1: MOTION AND FORCE level You can use the force probe to apply known forces to an object. You can also use the motion rectangular detector, brass pieces as in to the increase previous cart s two mass labs, to to 1 kg examine the motion of the object. In this way low-friction you will pulley, be able lightweight to explore string, the variety relationship of hangingbetween masses motion and force. You will need the following additional materials: motion cart motion detector motion cart 2-m motion rectangular track brass piece 2-m motion track table clamp level table clamp rectangular brass pieces to increase cart s mass to 1 kg Activity 1-1: low-friction Pushing and pulley, Pulling lightweight a Cart string, variety of hanging masses In thisactivity activity you 1-1: will Pushing move aand low-friction Pulling cart a Cart by pushing and pulling it with your hand. You will measure In this the activity force, you velocity, will and move acceleration. a low-friction Thencart you will by pushing be able toand lookpulling for mathematical it with your hand. relationships You will between measure the the net force, appliedvelocity, force and and theacceleration. velocity and acceleration, Then you will to see be whether able to look for eithermathematical is (are) related torelationships the force. between the net applied force and the velocity and acceleration, to see whether either is (are) related to the force. 1. Set up the cart, force probe, and motion detector on the 2-m track as shown below. The 1. Set up the cart, force probe, and motion detector on the 2-m track as shown below. cart should have a mass of about 1 kg with force probe included. Use the specially The cart should have a mass of about 1 kg with force probe included. Use the constructed thin brass pieces to place in the tray on top of the force probe to reach 1 kg total specially mass. The constructed motion sensor thin should brass be pieces set to to narrow place in beam. the tray Ask on your top TA of if the you force have probe to trouble reach finding 1 kg the total switch. mass. The motion sensor should be set to narrow beam. Ask your TA if you have trouble finding the switch. Motion Detector The force probe should be fastened securely to the cart so that its body and cable do not The force probe should be fastened securely to the cart so that its body and cable do not extend beyond the end of the cart facing the motion detector. [You may want to tape the extend beyond the end of the cart facing the motion detector. [You may want to tape the force probe cable back along the body to ensure that it will not be seen by the motion force probe cable back along the body to ensure that it will not be seen by the motion detector.] detector. Also carry the cable along with the force probe to avoid additional friction and Note: drag.] The force probe must be zeroed before each measurement. There is a small button labeled TARE on the side that you press to set the zero. Make sure you do this with nothing connected to the probe s hook.

3 Lab 4 Force and Motion L4-3 NOTE: The force probe must be zeroed before each measurement. There is a small button labeled TARE on the side that you press to set the zero. Make sure you do this with nothing connected to the probe s hook. Prediction 1-1: Imagine that you grasp the force probe hook and move the cart forward and backward in front of the motion detector. Do you think that either the velocity or the acceleration graph will look like the force graph? Is either of these quantities related to force? [That is to say, if you apply a changing force to the cart, will the graph of the velocity or acceleration resemble the graph of the force?] Discuss. Test your predictions: 2. Open the experiment file called L Motion and Force. This will set up velocity, force, and acceleration axes with a convenient time scale of 5 s. NOTE: When moving the cart, pull and push the force probe hook along a straight line parallel to the track. Do not twist the hook. Be sure that the cart never gets closer than 20 cm to the motion detector. 3. Verify that the motion detector sees the cart during its complete motion. 4. Zero the force probe as described previously. Grasp the force probe hook and begin graphing. When you hear the clicks, quickly pull the cart away from the motion detector and let go. Let the cart roll on its own for a couple of seconds, then quickly stop it by pushing on the hook. 5. Print out one copy of the graph for your group and include it with your report. Question 1-1: Does either graph velocity vs. time or acceleration vs. time resemble the force vs. time graph? Which one? Discuss. Question 1-2: Based on your observations, does it appear that there is a mathematical relationship between either applied force and velocity, applied force and acceleration, both, or neither? Discuss.

4 L4-4 Lab 4 Force and Motion Activity Activity1-2: 1-2: Speeding SpeedingUp Up You have seen in in the the previous previous activity activity that force that and force acceleration and acceleration seem to be seem related. to be Now related. we Now will examine we will the examine relationship the relationship between force between and acceleration force and more acceleration carefully. more carefully. Motion Sensor >20 cm 1. Set 1. Set up up the the track, track, pulley, cart, string (about 2 meters), motion detector, and force probe as shown as shown above. The track should be be level. level. The The cart should cart should be the be same the mass same as mass beforeas before (about (about 1 kg). 1 kg). Make Make sure that sure thethat forcethe probe force body probe and cable body do and not cable extendo beyond not extend the beyond back of the the back cart, of and the tape cart, theand cable tape back the along cable theback bodyalong to assure the that body theto motion assure detector that the motion sees Lab 4 detector - Force only& the Motion sees cart. only the cart. L04-5 Prediction 1-2: Suppose that you have a cart with very little friction and you pull this cart with a constant Prediction force. 1-2: Sketch Suppose onthat theyou axes have below a cart the with constant very little force friction and your and you predictions pull this of cart with a constant force. Sketch on the axes below the constant force and your the velocity time and acceleration time graphs of the cart s motion. predictions of the velocity time and acceleration time graphs of the cart s motion. 2 + PREDICTION University of Virginia Physics 0 Department 0 PHYS 1429, Spring Time (s) Prepare to graph velocity, acceleration, and force. Open the experiment file called 2. Prepare L to graph Speeding velocity, Up to acceleration, display the force, and velocity force. Open and acceleration the experiment axes. file called L Speeding 3. Hang a Up 20 g tomass display on the thestring. force, velocity and acceleration axes. 3. Hang Mass 35 of g masses hanging on weight: the string. 4. Zero the force probe with the string hanging loosely so that no force is applied to the Mass probe. of hanging Zero it weight: again before each graph. g 5. Begin graphing. Release the cart after you hear the clicks of the motion detector. Be University of sure Virginia that the Physics cable from Department the force probe is not Modified seen by from the motion P. Laws, detector, D. Sokoloff, and that R. it Thornton PHYS 1429, doesn t Springdrag 2014or pull the cart. Repeat until you get good graphs in which the cart is seen by the motion detector over its whole motion. Leave these data on the screen. Do not erase them.

5 Lab 4 Force and Motion L Zero the force probe with the string hanging loosely so that no force is applied to the probe. L04-6 Zero it again before each graph. Lab 4 - Force & Motion 5. Begin graphing. Release the cart after you hear the clicks of the motion detector. Be sure that6. theif cable necessary, from theadjust force probe the axes is notto seen display by the the motion graphs detector, more and clearly. that it doesn t Do not erase your drag ordata; pull the you cart. will Repeat need it until later. you get good graphs in which the cart is seen by the motion detector over its whole motion. Leave these data on the screen. Do not erase them. Question 1-3: After the cart is moving, is the force that is applied to the cart by the string 6. If necessary, constant, adjust increasing, the axes or decreasing? to display theexplain graphs more based clearly. on your Dograph. not erase your data; you will need it later. Question 1-3: After the cart is moving, is the force that is applied to the cart by the string constant, increasing, or decreasing? Explain based on your graph. Question 1-4: How does the acceleration graph vary in time? Does this agree with your prediction? Does a constant applied force produce a constant acceleration? Question 1-4: How does the acceleration graph vary in time? Does this agree with your prediction? Does a constant applied force produce a constant acceleration? Question 1-5: How does the velocity graph vary in time? Does this agree with your Question 1-5: How does the velocity graph vary in time? Does this agree with your prediction? What kind of change in velocity corresponds to a constant applied force? prediction? What kind of change in velocity corresponds to a constant applied force? 7. Accelerate the cart with a larger force than before. To produce a larger force, hang a mass 7. Accelerate the cart with a larger force than before. To produce a larger force, hang a two times as large as in the previous activity. mass about two times as large as in the previous activity. Mass of hanging weight: g 8. Graph force, Mass velocity, of hanging and weight: acceleration as before. Keep your previous data and these data. You 8. can Graph choose force, to display velocity, or not and display acceleration data under as the before. data tab Keep (with your arrow). previous You can data and these delete any other tries you make. Don t forget to zero the force probe with nothing attached data. You can choose to display or not display data under the data tab (with arrow). to the hook right before graphing. You can delete any other tries you make. Don t forget to zero the force probe with 9. Print out nothing one setattached of graphsto for the your hook group right andbefore includegraphing. them your report. 10. Use9. theprint linearout fit on one the set velocity of graphs graph for toyour measure group theand average include acceleration them in (slope your report. of the best10. fit line) Use and the the statistics feature,, of the the software to measure to measure the average the average force force and for the two average sets of acceleration good data you for have the with cart different for the two masses sets (click-and-drag of good data ayou rectangle have to with different select amasses region). (click-and-drag Record your measured a rectangle valuesto inselect Table 4.1. a region). Find therecord values only your during measured values the timein intervals Table 2-1. whenfind the force the and mean acceleration values only areduring nearly the constant. time intervals when the force and acceleration are nearly constant. PHYS 1429, University Spring 2014 of Virginia Physics Department PHYS 1429, Spring 2011

6 L4-6 Lab 4 Force and Motion Hanging Mass (g) Average force (N) Average acceleration (m/s 2 ) Table 4.1: Question 1-6: The average applied force increased because the gravitational force due to the hanging mass increased. Does there seem to be a simple mathematical relationship between the applied force and the average acceleration? Describe the relationship using an equation and using words. Comment: The mathematical relationship that you have been examining between the acceleration of the cart and the applied force is known as Newton s second law. INVESTIGATION 2: Force, Mass and Acceleration In previous activities you have applied forces to a cart having the same mass in each case and examined its motion. But when you apply a force to an object, you know that the object s mass has a significant effect on its acceleration. For example, compare the different accelerations that would result if you pushed a 1,000 kg (metric ton) automobile and a 1-kg cart, with the same force! In this investigation you will explore the mathematical relationship between acceleration and mass when you apply the same constant force to carts of different mass. You will not need any additional materials. Activity 2-1: Acceleration and Mass You can easily change the mass of the cart by attaching masses to it, and you can apply the same force each time by using a string attached to appropriate hanging masses. By measuring the acceleration of different mass carts, you can find a mathematical relationship between the acceleration of the cart and its mass, when the force applied by the string is kept constant. 1. Make sure that the force probe is fastened securely to the cart. [The cable must not interfere with the motion of the cart and must not be seen by the motion detector.] 2. We will define a mass scale in which the unit is the mass of the cart (including the force probe and flat brass piece), called one cart mass. We will add the rectangular black masses that should each be 0.5 cart masses. You may use an electronic balance to check, but note that it is limited to 600 g. Assemble masses that you can add to the cart to make the cart s mass equal to 1.5, 2.0, 2.5, and 3.0 cart masses. The black rectangular masses should be 0.5 cart masses. 3. Now add enough masses to make the cart s mass 2.0 cart masses.

7 Assemble masses that you can add to the cart to make the cart s mass equal to 1.5, 2.0, 2.5, and 3.0 cart masses. The black rectangular masses should be 0.5 cart masses. Lab 4 Force and Motion L Now add enough masses to make the cart s mass 2.0 cart masses. 4. Continue 4. Continue to use tothe usehanging the hanging masses masses that that you you used usedlast lastin inactivity Open 5. Open the experiment the experiment file called file called L Acceleration and Mass. 6. As 6. always, As always, zero the zeroforce the force probe probe before before each each graph graph with with nothing nothing pulling pullingon onit. it. Begin graphing. graphing. Release Release the cart the cart from from rest rest when whenyou youhear the clicks of the motion detector. Do not Do erase not erase your your data. data. You You can can hide hide it it using the Data icon,. 7. Use 7. the Usemouse the mouse to highlight to highlight the the time time interval during which the the acceleration is nearly is nearly constant on on your graph. Use the the linear statistics fit of the features velocityof graph the software to find theto average measure acceler- the constant average ation force andexperienced the statistics features by the cart of the and software average to acceleration measure the average during force the same experienced time interval. by the Record cart. Make your measured to do these values measurements for average forforce the same and time average interval. acceleration Record your in the third measured row of values Table for 4-1 average for 2.0 force cart and masses. average acceleration in the third row of Table 4.2 for 2.0 cart masses. Table 4-1 Mass of cart Average applied force (N) Average acceleration (m/s 2 ) Mass of cart Average applied force Average acceleration 1.0 ( cart masses ) (N) (m/s 2 ) Table 4.2: 8. Now 8. we Nowwant we want to repeat to repeat your your measurements with 1.0, 1.0, 1.5, 1.5, 2.5, 2.5, and and 3.0 cart 3.0 masses. cart masses. Do not Do not yet yet start. Arrange the masses the masses so you so have you 1.0 have cart 1.0 masses. cart masses. Comment: You want to accelerate the cart with the same applied force. As you may have noticed, Comment: the force You applied want to to accelerate the force the probe cart with by thestring same applied decreases force. once As the youcart mayis have released. [You noticed, will theexplore force applied why to this theis force so in probe a later by the lab.] string This decreases oncedepends the cart is on released. the size of the [You acceleration. will explorehowever, why this is we sodo in anot later want lab.] to This change decrease the hanging depends on mass theeven size of if the the applied acceleration. force changes However, a little. weit dois not approximately want to changeconstant. the hanging mass even if the applied force changes a little. It is approximately constant. 9. Before each measurement, zero the force probe with no force on it. Graph the motion of the 9. Before cart. (Don t each measurement, forget to zero zero the the force force probe first.) withmeasure no force on the it. average Graph force the motion and average of the acceleration cart. (Don tof forget the tocart zeroduring the force the probe time first.) interval Measure when the average the force force and acceleration averageare acceleration nearly constant of the cart and during record thethese time interval values in when the the first force row and of Table acceleration 4-1. are nearly constant and record these values in the first row of Table Repeat for masses of 1.5, 2.5 and 3.0 cart masses. 10. Repeat for masses of 1.5, 2.5 and 3.0 cart masses. 11. Print out one set of graphs for your group report. 11. Print out one set of graphs for your group report. Activity 2-2: Relationship Between Acceleration and Mass PHYS 1429, Spring Plot a graph of average acceleration vs. cart mass (with an approximately constant applied force). You can do this by opening the experiment file called L Avg. Accel. vs. Mass. Enter the acceleration and mass data into the table on the screen. You may wish to adjust the axes to better display the data.

8 L4-8 Lab 4 Force and Motion Question 2-1: Does the acceleration of the cart increase, decrease, or remain the same as the mass of the cart is increased? Comment: We are interested in the nature of the mathematical relationship between average acceleration and mass of the cart, with the applied force kept constant. As always, this can be determined from the graph by drawing a smooth curve which fits the plotted data points. 2. Use the fit routine in the software to fit the data on your graph of average acceleration vs. mass of the cart. Select various possible relationships and test them. 3. When you have found the best fit, print the graph along with the fit equation for your group report. Question 2-2: What appears to be the mathematical relationship between acceleration and mass of the cart, when the applied force is kept constant? Question 2-3: If the combined force is F, the cart mass is M, and the acceleration is a, write a mathematical relationship that relates these three physical quantities.

9 Lab 4 Force and Motion L4-9 INVESTIGATION 3: Tension at Bottom of Pendulum Swing We now consider the following question: If we let a weight swing in a pendulum motion, what will happen to the tension in the string at the moment the pendulum is at the bottom of its motion? To answer this question, we need to know the acceleration of the pendulum at the bottom of its motion. This is in the direction of the change in velocity. Prediction 3-1: Sketch a pendulum swinging from left to right. In what direction is the velocity just before it reaches the bottom? Indicate with a vector on the sketch. What about just after it passes the bottom? Indicate with a vector on the sketch. Now combine these to find the acceleration at the bottom of the swing. Draw the resulting vector on the sketch. Prediction 3-2: In what direction must the total force on the pendulum be at the bottom of its swing? Explain. Prediction 3-3: Given your answer to Prediction 3-2 and that the weight of the pendulum is downward, how must the upward force (i.e. the tension in the string) compare to the weight of the pendulum, when at the bottom of its swing? 1. Hang a 100 g mass from the string and hold the cart so that there is about 1 meter of string between the pulley and the weight. 2. Open the file called L Pendulum Swing. With no tension in the string, zero the force probe and then let the weight hang motionless from the string. 3. Begin graphing. You should observe a flat line, indicating the weight of the hanging mass. What will happen to the reading if the tension in the string increases? Test this by gently pulling downward on the weight. Stop graphing. Clear all data. 4. With the hanging weight motionless, graph for a few seconds to show the weight of the pendulum. Stop graphing, but don t clear the data. 5. Pull the pendulum back about 30. Release and begin graphing.

10 L4-10 Lab 4 Force and Motion 6. Observe both the swinging weight and the graph and note what the force is at the bottom of the swing. You will probably have to work together to do this. Have the probe watcher call out mark at the bottom of the swing. 7. Stop after a few swings. 8. Print out a graph for your group. Indicate the different parts of the pendulum cycle. Question 3-1: Was your Prediction 3-3 confirmed? Discuss. Please clean up your lab area