Lab 6 - Gravitational and Passive Forces

Transcription

1 Lab 6 Gravitational and Passive Forces L6-1 Name Date Partners L06-1 Lab 6 - Gravitational and Passive Forces Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies And thusby Nature the attraction will beof very gravity conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the Isaac attraction Newton of gravity OBJECTIVES Isaac Newton To explore the nature of motion along a vertical line near the Earth s surface. OBJECTIVES To extend the explanatory power of Newton s laws by inventing an invisible force (the gravitational force) that correctly accounts for the falling motion of To explore the nature of motion along a vertical line near the Earth s surface. objects observed near the Earth s surface. To extend examine the explanatory the magnitude power of Newton s the acceleration laws by inventing of a falling an invisible object under force (the the influence gravitational of force) the gravitational that correctlyforce accounts near for the the Earth s fallingsurface. motion of objects observed near the Earth s surface. To examine the motion of an object along an inclined ramp under the influence of the To examine gravitational the magnitude force. of the acceleration of a falling object under the influence of the To gravitational incorporate force frictional near the forces Earth sinto surface. Newton s first and second laws of motion. To examine explore interaction the motion of forces an object between alongobjects an inclined as described ramp under by Newton s the influence third of the law of gravitational motion. force. To To incorporate explore tension frictional forces. forces into Newton s first and second laws of motion. To apply Newton s laws of motion to mechanical systems that include tension. To explore interaction forces between objects as described by Newton s third law of motion. OVERVIEW You started To explore your tension study of forces. Newtonian dynamics in Lab 4 by developing the concept of force. Initially, when asked to define forces, most people think of a force as an obvious push or To pull, apply such Newton s as a punch laws ofto motion the jaw to mechanical or the tug systems of a rubber that include band. tension. By studying the acceleration that results from a force when little friction is present, we came up with a second OVERVIEW definition of force as that which causes acceleration. These two alternative definitions You started of your force study do not of Newtonian always appear dynamics to be inthe Lab same. 4 by Pushing developing on the a wall concept doesn t of force. seem to Initially, cause the when wall asked to move. to define An forces, object most dropped people close think to of the a force surface as an of obvious the Earth push accelerates or pull, and such yet as there a punch is no tovisible the jawpush or theor tug pull of aon rubber it. band. By studying the acceleration that results from a force when little friction is present, we came up with a second definition of force as that which causes acceleration. These two alternative definitions of force do not always appear to be University University of of Virginia Virginia Physics Physics Department Department PHYS PHYS 1429, 1429, Spring Spring Modified from from P. P. Laws, Laws, D. D. Sokoloff, R. R. Thornton

2 L6-2 Lab 6 Gravitational and Passive Forces L06-2 Lab 6 - Gravitational & Passive Forces the same. Pushing on a wall doesn t seem to cause the wall to move. An object dropped close to the surface of the Earth accelerates and yet there is no visible push or pull on it. The genius of Newton was to recognize that he could define net force or combined force The genius of Newton was to recognize that he could define net force or combined force as as that which causes acceleration, and that if the obvious applied forces did not account that which causes acceleration, and that if the obvious applied forces did not account for the for the degree of acceleration then there must be other invisible forces present. A prime degree of acceleration then there must be other invisible forces present. A prime example of example of an invisible force is the gravitational force the attraction of the Earth for an invisible force is the gravitational force the attraction of the Earth for objects. objects. When an object falls close to the surface of the Earth, there is no obvious force being applied When to it. an Whatever object is falls causing close the to object the surface to move of is the invisible. Earth, Most there people is no obvious rather casually force refer being applied to the cause to it. of Whatever falling motions is causing as the the action object of gravity. to move What is invisible. is gravity? Most Can people we describe rather casually gravity as refer justto another the cause force? of Can falling we describe motions its as effects the action mathematically? of gravity. CanWhat Newton s is gravity? laws Can be interpreted we describe in suchgravity a way that as they just cananother be used force? the mathematical Can we prediction describe of its motions effects mathematically? that are influencedcan by gravity? Newton s laws be interpreted in such a way that they can be used for the mathematical prediction of motions that are influenced by gravity? It almost seems that we have to invent an invisible gravitational force to save Newton s second It almost law. seems Since that objects we have near to invent the surface an invisible of the gravitational Earth fall force with to a constant save Newton s acceleration, second we law. will Since use objects Newton s nearsecond the surface law of to the show Earththat fallthere with amust constant be a acceleration, constant (gravitational) we will use force Newton s acting second the law object. to show that there must be a constant (gravitational) force acting on the object. Finding invisible forces (forces without an obvious agent to produce them) is often hard because Finding some invisible of forces them (forces are not without active anforces. obvious agent Rather, to produce they are them) passive is often forces, hard because such as normal some offorces, them are which not active crop forces. up only Rather, in response they are passive to active forces, ones. such as (In normal the case forces, of which normal forces, crop upthe only active in response forces are to active ones ones. like the (In the push case you ofexert normal on forces, a wall the or active the gravitational forces are ones pull on like a book the push sitting you on exert a table.) on a wall or the gravitational pull on a book sitting on a table.) Frictional and tension forces are other examples of passive forces. The passive nature of friction Frictional and tension forces are other examples of passive forces. The passive nature of is obvious when you think of an object like a block being pulled along a rough surface. There is friction is obvious when you think of an object like a block being pulled along a rough an applied force (active) in one direction and a frictional force in the other direction that opposes surface. There is an applied force (active) in one direction and a frictional force in the the motion. If the applied force is discontinued, the block will slow down to rest but it will not other direction that opposes the motion. If the applied force is discontinued, the block start moving in the opposite direction due to friction. This is because the frictional force is will passive slow and down stops to acting rest but as soon it will as not the block start moving comes to in rest. the opposite direction due to friction. This is because the frictional force is passive and stops acting as soon as the block comes to Likewise, rest. tension forces, such as those exerted by a rope pulling on an object can exist only when there is an active force pulling on the other end of the rope. Likewise, tension forces, such as those exerted by a rope pulling on an object can exist only In this when lab you there will is first an active study vertical force pulling motion on and the the other gravitational end of the force. rope. Then you will examine the motion of an object along an inclined ramp. You will use Newton s laws of motion as a In working this lab hypothesis you will to first invent study frictional vertical motion and tension and forces. the gravitational Along the way force. youthen will examine you will examine Newton sthe third motion law of of motion. an object along an inclined ramp. You will use Newton s laws of motion as a working hypothesis to invent frictional and tension forces. Along the way you INVESTIGATION will examine Newton s 1: third Motion law of and motion. Gravity PHYS University 1429, of Spring Virginia 2011 Physics Department

3 Lab 6 Gravitational Lab 6 and - Gravitational Passive & Forces Passive Forces L6-3 L06-3 INVESTIGATION 1: MOTION AND GRAVITY Let s begin the study of the phenomenon of gravity by examining the motion of an object such as Let s a ball begin when the study it is allowed of the phenomenon to fall vertically of gravity nearby the examining surface the of the Earth. This study motion isof not an easy, object because such as the a ball motion when happens it is allowed veryto quickly! fall vertically You near the surface of the Earth. This study is not easy, because the motion can first predict what kind of motion the ball undergoes by tossing a ball in the happens very quickly! You can first predict what kind of motion the ball laboratory several undergoes times and by seeing tossing what a ball you in the think laboratory is goingseveral on. times and seeing A falling motion what is too you fast think to is observe going on. carefully by eye. You will need the aid of the motion detector A falling and motion computer is too to fast examine to observe thecarefully motionby quantitatively. eye. You will Fortunately, the motion the aid detector of the can motion do measurements detector and computer just fastto enough examine to graph the motion this need quantitatively. Fortunately, the motion detector can do measurements motion. To carry just out fast your enough measurements to graph this you motion. will need To carry out your measurements you will need motion detector motion detector basketball table clamps, rods, etc. 3 m tape measure softball 4 x 4 wood block table clamps, rods, etc. Activity 1-1: Motion of a Falling Ball 3 m tape measure Prediction 1-1: Suppose that you drop the ball from height of about 2 m above the floor, releasing it from rest. On the axes that follow, sketch your predictions for the velocity 4 x 4 wood block time and acceleration time graphs of the ball s motion. Assume that the positive y direction is upward. Activity 1-1: Motion of a Falling Ball PHYS , Spring 2011 PREDICTION Prediction 1-1: Suppose that you drop the ball from height of about 2 m above the floor, releasing it from rest. On the axes that follow, sketch your predictions for the velocity time 0 and acceleration time graphs of the ball s motion. Assume that the positive y direction is upward. - Acceleration Velocity 2 Acceleration Velocity Time (s) Test 0 your predictions. 1 You have 2 previously 3 used the motion 4 detector to 5 examine the motion of your body and of a cart. The motion of a falling ball takes place much faster PREDICTION Time (s) Test your predictions. You have previously used the motion detector to examine the motion of your body and of a cart. The motion of a falling ball takes place much faster. While you can use the motion detector to measure position, velocity, and acceleration, you will have to collect data at a faster rate than you have before.

4 L6-4 Lab 6 Gravitational and Passive Forces The easiest way to examine the motion of the falling ball is to mount the motion detector as high up as you can and to use a large ball that is not too light (like a basketball rather than a beach ball). It is essential to keep your hands and the rest of your body out of the way of the motion detector after the ball is released. This will be difficult and may take a number of tries. It also will take some care to identify which portions of your graphs correspond to the actual downward motion of the ball and which portions are irrelevant. 1. Use the table clamps, rods, and right angle devices to attach the motion detector, about 2 m above the floor, with the detector looking straight downward, as shown on the right. 2. Set the motion detector on the wide setting. 3. Open the experiment file called L Falling Ball. The axes will look similar to the ones on which you made your predictions. This experiment file will also set the data collection to a faster rate than has been used before (30 points/s). Because the motion detector is pointing downward - in the negative y direction the software has been set up to make distance away from the detector negative. 4. Hold the ball at least 20 cm directly below the motion detector and at least 180 cm above the floor. Remember that your hands and body must be completely out of the path of the falling ball, so the detector will see the ball and not your hands or body the whole way down. 5. When everything is ready, begin graphing and release the ball as soon as you hear the clicks from the motion detector. 6. Adjust the axes if necessary to display the velocity and acceleration as clearly as possible. Do not erase the data so that the graphs can be later used for comparison. 7. Print one set of graphs for your group and include them with your report. 8. Use the mouse to highlight the time interval during which the ball was falling freely. Question 1-1: What does the nature of the motion look like constant velocity, constant acceleration, increasing acceleration, decreasing acceleration, or other (describe, if other)? Discuss how your observations compare with your predictions.

5 Lab 6 Gravitational and Passive Forces L6-5 Question 1-2: Is the acceleration of the ball positive or negative as it falls? Does this sign agree with the way that the velocity appears to be changing on the velocity-time graph? Discuss. Activity 1-2: The Magnitude of Gravitational Acceleration As you saw in Lab 3, you can find a value for the average acceleration in various ways. One method is to read the average value from the acceleration - time graph. Another is to find the slope of the velocity time graph. 1. Use the statistics features of the software to read the average value of the acceleration during the time interval from just after the ball began falling (beginning of uniform acceleration) to just before the ball stopped falling (end of uniform acceleration). Average acceleration: ± m/s 2 2. Use the fit routine to find the mathematical relationship between velocity and time during the same time interval as in step 1. Write below the equation you find from the fit that relates velocity (v) to time (t). 3. From the equation in step 2, what is the value of the acceleration? Average acceleration: ± m/s 2 Question 1-3: Discuss how well the two values for the gravitational acceleration agree with each other. Activity 1-3: Motion Up and Down Prediction 1-2: Suppose that you toss a ball upward and analyze the motion as it moves up, reaches its highest point, and falls back down. Is the acceleration of the ball the same or different during the three parts of the motion moving upward, momentarily at the highest point, and moving downward? Explain.

6 the highest point, and moving downward? Explain. Moving L6-6 upward: Lab 6 Gravitational and Passive Forces Moving upward: Momentarily at highest point: Momentarily at highest point: Moving Moving downward: downward: Prediction 1-3: Sketch on the axes below your predictions of the velocity - time and Prediction 1-3: Sketch on the axes below your predictions of the velocity - time and acceleration time graphs for the entire motion of the ball from the moment it leaves your acceleration - time graphs for the entire motion of the ball from the moment it leaves your hand going up until just before it returns to your hand. Assume that the positive direction hand going up until just before it returns to your hand. Assume that the positive direction is upward. is upward. 2 + PREDICTION Time when ball reaches highest point Time 4 5 Throwing the ball upward and keeping it in the range of the motion detector is harder to do Throwing than dropping the ball the upward ball. and Try keeping to throw it in the range ball up of directly the motion under detector the is motion harder detector. to do than It dropping the ball. Try to throw the ball up directly under the motion detector. It may take a may take a number of tries. Again be sure that your body is not seen by the motion number of tries. Again be sure that your body is not seen by the motion detector. detector. 1. The same experiment file L Falling Ball used in Activity 1-1 should work in this University activity of Virginia as well. Physics You Department can keep the graphs from Modified Activity from 1-1 P. on Laws, the D. screen Sokoloff, if you R. desire. Thornton PHYS 1429, Spring 2011 The new data will be in a different color. You can also click on the Data icon and choose not to display a particular data run. 2. When everything is ready, begin graphing, and when you hear the clicking begin, toss the ball up toward the motion detector. Toss the ball as high as you can, but remember that it should never get closer than 20 cm below the motion detector. A short quick throw will work best. Repeat until you get a throw where you are sure the ball went straight up and down directly below the detector. You can choose under Experiment to delete the last data run if you do

7 Lab 6 Gravitational and Passive Forces L6-7 not want to keep it. You can also click on a graph and use the DELETE key to remove it. You may need to make several tries before you decide to keep the data. Let all group members try, if you have time. 3. When you obtain a good run, print one set of graphs for your group and include them in your report. 4. Label the portions of the printed graphs that show the ball s up and down motion. Also label with an arrow the instant in time when the ball reached its highest point. Question 1-4: Qualitatively compare the acceleration during the three parts of the motion on the way up, at the highest point, and on the way down. Discuss your observations based on the sign of the change in velocity. How well do you observations agree with your predictions? On the way up: At the highest point: On the way down: Question 1-5: There is a common idea that the acceleration of the ball must be zero when it stops. If this were true, could the velocity of the ball change L06-8 once it stopped? Discuss. Activity 1-4: Vertical Motion with Air Resistance Activity 1-4 (Optional): Vertical Motio In this Activity you will use the motion filter falling from rest. In addition to the a flat-bottomed paper coffee filter - th In this Activity you will use the motion detector to examine the motion of a paper coffee filter falling from rest. In addition to the setup in Activity 1-1 you will need a flat-bottomed paper coffee filter - the type with folds along the sides 1. Use the experiment file L Falling Filter. As usual, wait until you hear the motion detector click and then release the coffee filter with the flat bottom facing down as shown on the left. If necessary, increase the time range to record the complete motion 1. Use the ex wait until release the shown on record the velocity a graphs mo a good gra side out of 2. Be sure to keep your body out of the 3. Print out one set of graphs and inclu

8 L6-8 Lab 6 Gravitational and Passive Forces of the filter and adjust the velocity and acceleration axes if necessary to display the graphs more clearly. It may take you several tries to obtain a good graph, because the coffee filter tends to float to the side out of range of the motion detector. 2. Be sure to keep your body out of the way of the motion detector. 3. Print out one set of graphs and include them with your report. Question 1-6: Compare the graphs to those for the falling ball. Does the filter also appear to fall with a constant acceleration? If not, how would you describe the motion? Is the velocity changing as the filter falls? If so, how? Question 1-7: Based on Newton s laws of motion, do you think that the gravitational force is the only force acting on the filter? If there is another force, what is its direction and how does its magnitude compare to the gravitational force? Discuss. Activity 1-5: Motion Along an Inclined Ramp Another common motion involving the gravitational force is that of an object along an inclined ramp. Prediction 1-4: Consider a very low-friction cart moving along an inclined ramp, as shown above. The cart is given a push up the ramp and released, and its motion is graphed using the motion detector at the top of the ramp. [The direction toward the motion detector is positive.] Sketch on the axes below your predictions of the velocity - time and acceleration - time graphs for the motion of the cart.

9 Lab 6 Gravitational and Passive Forces L PREDICTION Acceleration Velocity Time (s) Prediction 1-5: How do you predict the magnitude of the acceleration of the cart will compare to the acceleration you determined in Activity 1-2 for a ball falling straight downward? Explain. To test your predictions, you will need in addition to the equipment used above motion cart (with no friction pad) 2-m motion track and support to raise one end about 10 cm 1. Set up the ramp with the motion detector at the high end. Use a wooden block to elevate one end of the ramp by 10 cm or so. Be sure that the motion detector sees the cart over the whole length of the ramp. 2. Open the experiment file called L Inclined Ramp to display the velocity time and acceleration time plots that were shown previously for Prediction 1-4. As before, the software has been set up to consider motion toward the detector positive so that the positive direction of motion is up the ramp. 3. Hold the cart at the bottom of the ramp and begin graphing. When you hear the clicks of the motion detector, give the cart a push up the ramp and release it. DO NOT PUSH THE CART HARD ENOUGH FOR IT TO HIT THE MOTION DETECTOR OR FALL OFF THE TRACK!! PRACTICE A COUPLE OF TIMES! The graph should include all three parts of the motion up the ramp, at its highest point, and on its way down and the cart should never get closer than 20 cm from the motion detector. Repeat until you have good graphs. Only keep your good data. 4. Print out one set of graphs for your group and include them with your report.

10 L6-10 Lab 6 Gravitational and Passive Forces 5. Use an arrow to mark the instant when the cart was at its highest point along the track on both the velocity and acceleration graph. 6. Use the statistics or the linear fit features of the software to measure the average acceleration of the cart during the time interval after it was released and before it was stopped at the bottom of the ramp. Average acceleration: ± m/s 2 Question 1-8: Did your graphs agree with your predictions? Does this motion appear to be with a constant acceleration? Question 1-9: How did the magnitude of the acceleration compare with that for the ball falling which you determined in Activity 1-2? Is this what you predicted? Was this motion caused by the gravitational force? Why isn t the acceleration the same as for the ball falling? Question 1-10: What fraction of the falling-ball acceleration did the cart experience? Is this what you would expect given the incline of the ramp? % INVESTIGATION 2: Newton s Laws when Friction is Present In previous labs we have worked hard to create situations where we could ignore the effects of friction. We have concentrated on applied forces involving pushes and pulls that we can see and measure directly. The time has come to take friction into account. You can make observations by applying a force directly to your force probe mounted on a block (with significant friction) and comparing the block s acceleration to the acceleration of the cart (with negligible friction). To make observations on the effects of friction you will need force probe motion detector

11 You can make observations by applying a force directly to your force probe mounted on a block Lab 6 Gravitational (with significant and Passive friction) Forcesand comparing the block s acceleration L6-11 to the acceleration of the cart (with negligible friction). To make string observations ( 30 cm. long the with effects loopsof onfriction each end). you will need! force 2-m probe motion track! 2-m motion track! motion detector! wood friction block wood friction block! string ( ~30 cm. long with loops on each end). Activity 2-1: 2-1: Static Staticand andkinetic Frictional Forces If the frictional force is equal in magnitude to the applied force, then according to Newton s If the frictional first law, forcethe is equal block inmust magnitude either toremain the applied at rest force, move then according with a constant to Newton s velocity. first law, the block must either remain at rest or move with a constant velocity. The frictional forces when two objects are sliding along each other are called kinetic frictional The frictional forces. forces If the when objects two objects are not are sliding sliding along each other other, are then called the kinetic frictional frictional forces forces. If the objects are not sliding along each other, then the frictional forces are called static are called static frictional forces. In this Activity you will examine whether the frictional frictional forces. In this Activity you will examine whether the frictional force is different when force is different when an object is at rest (static friction) than when it is sliding along a an object is at rest (static friction) than when it is sliding along a track (kinetic friction). track (kinetic friction). Prediction 2-1: A block is sitting on a table, as shown above. You pull on a string Prediction 2-1: A block is sitting on a table, as shown above. You pull on a string attached to the block, and the block doesn t move because the frictional force opposes attached to the block, and the block doesn t move because the frictional force opposes your pull. You pull harder, and eventually the block begins to slide along the table top. How PHYS does1429, the frictional Spring 2011 force just before the block started sliding compare to the frictional force when the block is actually sliding? Explain. You can test your prediction by mounting the force probe on a wooden block and pulling the block along the table top (not on the aluminum track). 1. Measure the mass of the block and force probe: Mass of block: kg. Mass of probe: kg 2. Set up the block, string, force probe and motion detector as shown below. Make sure that the wood side of the block is down. Set the force probe on top of the friction block. Place all four 1/2 kg masses on the force probe to make the overall mass about 2.5 kg. 3. Prepare to graph velocity and force by opening the experiment file called L Static and Kinetic Friction.

12 L6-12 Lab 6 Gravitational and Passive Forces 4. Zero the force probe with nothing pulling on it. Begin graphing with the string loose, then gradually pull very gently on the force probe with the string and increase the force very slowly. Be sure that you pull horizontally not at an angle up or down. When Lab 6 - Gravitational & Passive Forces L06-13 the block begins to move, pull only hard enough to keep it moving with a small velocity, which is as constant (steady) as possible. Question 5. Do 2-1: not erase Does your the data block so that feel you a force can useon them it due for comparison to the string, withand those yet in not move? Why? Activity What happens 2-2. Do not to the yet print frictional out the force data. just as the block begins to slide? Does this agree with your prediction? Explain. Question 2-1: Does the block feel a force on it due to the string, and yet not move? Why? What happens to the frictional force just as the block begins to slide? Does this agree with your prediction? Explain. Question 2-2: Note the time on your force graph when the block just began to slide (you ll mark it later after you ve printed the graphs). From the graph, how do you know Question 2-2: Note the time on your force graph when the block just began to slide when this time is? (you ll mark it later after you ve printed the graphs). From the graph, how do you know when this time is? Activity Activity 2-2: 2-2: Frictional Frictional Force Force and and Normal Normal Force Force The frictional force is nearly the same regardless of how fast the object moves, but there is The usually frictional a difference force is nearly between the same static regardless and kinetic of how frictional fast theforces. object moves, Now you but there will examine is usually frictional a difference forces between depend static on and the kinetic force between frictional forces. the surface Now you and will the examine object ifthe frictional normal if force. forces depend on the force between the surface and the object the normal force. All Allof ofthe forces exerted on on a block a block being being pulled pulled on aon table a table top are top shown are shown in the diagram in the diagram below. below. Surfaces Surfaces like a wall like or a table wall top or a can table exert top a force can perpendicular exert a force to perpendicular the surface called to the a normal surface called force. a Innormal the caseforce. of the block In the on case the table, of the block table exerts on the a normal table, force the table upward exerts on the a block, normal force and the upward Earth exerts on the a block, gravitational and the force Earth (the exerts weight a ofgravitational the block) downward force (the on the weight block. of the block) downward on the block. Since we know that the block doesn t move up or down as it sits at rest or slides along the Since table s we know surface, that the block combined doesn t (net) movevertical up or down force asmust it sits be at rest zero oraccording slides alongto the Newton s table s first surface, law. theso combined the magnitude (net) vertical of the force normal must be force zeromust according just to equal Newton s the magnitude first law. Sof the the gravitational magnitude offorce. the normal Using force the must symbols just equal in the the diagram, magnitude we of obtain the gravitational force. Using the symbols in the diagram, we obtain FG = FN = mg where m is the total mass of the object, and g is the gravitational acceleration, 9.8 m/s 2.

13 Lab 6 Gravitational and Passive Forces L6-13 F G = F N = mg where m is the total mass of the object, and g is the gravitational acceleration, 9.8 m/s 2. Prediction 2-2: If you change the normal force exerted by the table on the block (by adding or removing masses from the force probe), what will happen to the frictional force? Explain. Test your prediction. Use the same setup and experiment file, L Static and Kinetic Friction, as in Activity Remove all but two of the 1/2 kg masses from the top of the force probe. [The new total mass should be about 1.5 kg.] 2. Zero the force probe with nothing pulling on it. The data from Activity 2-1 is still being displayed on the computer screen. As in Activity 2-1, begin graphing with the string loose, then gradually pull very gently on the force probe with the string, and increase the force very slowly. Be sure that you pull horizontally not at an angle up or down. When the block begins to move, pull only hard enough to keep it moving with a small velocity that is as constant (steady) as possible. 3. Both sets of data with different masses should be displayed. Question 2-3: Compare the two sets of graphs. In what ways are they similar, and in what ways are they different? Are the kinetic frictional forces the same or different? Discuss. 4. Add 2 more 1/2 kg masses [for a total of about 2.5 kg] and repeat the measurement. 5. For each of the runs, use the statistics or linear fit features of the software to measure the average frictional forces during the time intervals when the block was moving with a constant velocity. Record the systems masses and frictional forces in the appropriate row of Table 6.1. [You can choose which run you are displaying by clicking on and off the Run # under the Data icon.] 6. Calculate the normal forces and the coefficient of friction (the ratio of the frictional force to the normal force: µ = F f / FN ) for each run and record in Table Print out one graph containing all these data for your group. Carefully mark on your graph the total mass for each set of data. 8. Use an arrow to mark the time on your force graph when the block just began to slide (see Question 2-2).

14 L6-14 Lab 6 Gravitational and Passive Forces System: block, force probe and mass kg masses kg masses Total Mass (kg) Normal force (N) Average kinetic frictional force (N) Coefficient of friction ± ± ± ± Table 6.1: Question 2-4: Discuss the assertion that µ is approximately constant. INVESTIGATION 3: Newton s Third Law All individual forces on an object can be traced to an interaction between it and another object. For example, we believe that while the falling ball is experiencing a gravitational force exerted by the Earth on it, the ball is exerting a force back on the Earth. In this investigation we want to compare the forces exerted by interacting objects on each other. What factors might determine the forces between the objects? Is there a general law that relates these forces? We will begin our study of interaction forces by examining the forces each person exerts on the other in a tug-of-war. Let s start with a couple of predictions. Prediction 3-1: Suppose that you have a tug-of-war with someone who is the same size L06-16 and weight as you. You both pull as hard as you can, and it is alab stand-off. 6 - Gravitational One of you & Passive might Forces move a little in one direction or the other, but mostly you are both at rest. Predict the relative magnitudes of the forces between person 1 and person 2. Place a Predict the relative magnitudes of the forces between person 1 and person 2. Place a check next check next to your prediction. to your prediction. Person 1 exerts a larger force on person 2. Person 1 exerts a larger force on person 2. The people exert the same size force on each other. Person 2 exerts Thea people larger exert force the on same person size1. force on each other. Prediction 3-2: Suppose Person 2now exerts that a larger you have force on a tug-of-war person 1. with someone who is much smaller and lighter than you. As before, you both pull as hard as you can, and it is a stand-off. One of you might move a little in one direction or the other, but mostly you are both at rest.

15 The check next to people your exert prediction. the same size force on each other. Lab 6 Gravitational and Passive Forces L6-15 Person Person 2 1 exerts exerts a larger larger force force on on person person Prediction The 3-2: people 3-2: Suppose exert the now same that size you force have on a a each tug-of-war other. with with someone someone who who is much is much smaller Person and lighter 2 exerts than a you. larger you. As before, As force before, on you person both you pull 1. both as pull hard as you hard can, as and you itcan, is a stand- it is a stand-off. One ofone youof might you move might a little move ina one little direction in one or direction the other, or but the mostly other, you but are mostly both at you are Prediction 3-2: Suppose now that you have a tug-of-war with someone who is much both rest. at rest. smaller and lighter than you. As before, you both pull as hard as you can, and it is a stand-off. One of you might move a little in one direction or the other, but mostly you are both at rest. Predict the relative magnitudes of the forces between person 1 and person 2. Place a check Predict next theto relative your prediction. magnitudes of the forces between person 1 and person 2. Place a check next to your prediction. Person Predict the relative 1 exerts magnitudes a larger force of the on person forces 2. between person 1 and person 2. Place a The check next to people your exert prediction. Person the 1same exertssize a larger force force on on each person other. 2. Person Person 2 1 exerts exerts a larger larger force force on on person person The people exert the same size force on each other. Prediction The 3-3: people Again, exert suppose the same that size you force have on each a tug-of-war other. with someone who is much Person 2 exerts a larger force on person 1. smaller Person and lighter 2 exerts than a you. larger This force time on person the lighter 1. person is on a skateboard, and with some Prediction effort you 3-3: are able to pull him or you her have along a tug-of-war the floor. Prediction 3-3: Again, suppose that you have a tug-of-war with with someone someone who is who much is much smaller and lighter than than you. you. This This time time the lighter the lighter person is person a skateboard, is on a skateboard, and with some and with some effort effort you are you able are to able pull to him pull or her him along or her the along floor with the floor. constant velocity. PHYS Predict 1429, thespring relative 2011 magnitudes of the forces between person 1 and person 2. Place a check next to your prediction. PHYS 1429, Spring 2011 Person 1 exerts a larger force on person 2. The people exert the same size force on each other. Person 2 exerts a larger force on person 1. To test your predictions you will need the following in addition to previously: another force probe (total of two) two 1 kg masses Activity 3-1: Interaction Forces in a Tug-of-War

16 1. Open the experiment file called L6-16 L Tug-of-War. The software will then be Lab 6 Gravitational and Passive Forces set up to measure the force applied to each probe with a data collection rate of 20 points per 1. Open the experiment file called L Tug-of-War. The software will then be set up second. to measure the force applied to each probe with a data collection rate of 20 points per 2. Since second. the force probes will be pulling in opposite directions in the tug-of-war, we have reversed the 2. Since sign of theone force of probes them. will be pulling in opposite directions in the tug-of-war, we have reversed sign of one of them. 3. When you are ready to start, zero both of the force probes. Then hook the force probes 3. When together, you arebegin ready to graphing, start, zeroand bothbegin of thea force gentle probes. tug-of-war. Then hook Pull the back force and probes forth while together, watching beginthe graphing, graphs. and Be begin sure anot gentle to exceed tug-of-war. a force Pullof back 50 and N. forth Do not while pull watchingsince the graphs. this might Be sure damage not to exceed the force a force probes. of 50 N. Do not pull too hard, since this might too hard, damage the force probes. 4. Print out one set of graphs for your group. 4. Print out one set of graphs for your group. Question 3-1: How did the two pulls compare to each other? Was one significantly different from the other? How did your observations compare to your predictions? Question 3-1: How did the two pulls compare to each other? Was one significantly different from the other? How did your observations compare to your predictions? INVESTIGATION 4: TENSION FORCES INVESTIGATION 4: Tension Forces When you pullon a rope attached to a crate, your pull is somehow transmitted down down the rope the torope the crate. to the Tension crate. is Tension the nameis given the to name forces given transmitted to forces along transmitted stretched strings, along stretched ropes, rubber strings, bands, ropes, springs, rubber and wires. bands, springs, and wires. Is the whole force you apply transmitted to the crate, or is the Is pull the at whole the other force end you larger apply or smaller? transmitted Does to it the matter crate, how or is long the the pull rope at the is? How other isend the force larger magically or smaller? transmitted Does matter along the how rope? long These the are rope some is? of the How questions is the youforce will examine in this investigation. University Obviously, of Virginia the ropephysics by itself Department is unable to exert a force Modified on the from crate P. Laws, if youd. are Sokoloff, not pulling R. Thornton on the PHYS other1429, end. Spring Thus, 2011 tension forces are passive just like frictional and normal forces. They act only in response to an active force like your pull. Prediction 4-1: If you apply a force to the end of a rope as in the picture above, is the whole force transmitted to the crate, or is the force at the crate smaller or larger than your pull? To test your prediction you will need the following in addition to what you already have: table clamp and rod string

17 Lab 6 Gravitational and Passive Forces L6-17 To test your prediction you will need the following in addition to what you already have: Activity 4-1: Mechanism of Tension Forces! table clamp and rod! string Activity 4-1: Mechanism of Tension Forces Open the experiment file file called called L L Tension Tension Forces. Forces. 2. Hold the the two two probes with with a string a string loop loop hanging hanging loosely loosely between between the hooks. the hooks. 3. Zero both both force force probes. probes. Begin Begin graphing, graphing, and pull and softly pull atsoftly first and at then first harder. and then Then harder. vary Then the vary applied the applied force back force andback forth. and Be sure forth. notbe to exceed sure not 50to N. exceed 50 N. 4. Print out one one set set of of graphs graphs for for your your group. group. Question 4-1: Based on the readings of the two force probes, when you pull on one end Question 4-1: Based on the readings of the two force probes, when you pull on one end of the string, is the force transmitted down to the other end? Explain. of the string, is the force transmitted down to the other end? Explain. 5. Indicate with arrows on the diagram above the directions of the forces exerted by the string on force probe 1 and on force probe Indicate with arrows on the diagram above the directions of the forces exerted by the string on force probe 1 and on force probe 2. Prediction 4-2: What happens when a string is hung around a pulley? Is the tension force still transmitted fully from one end of the string to the other? PHYS 1429, Spring 2011 To test your prediction, in addition to the equipment listed above you will need low-friction pulley 2-m motion track level low friction cart long piece of string Activity 4-2: Tension When a String Changes Direction 1. Attach force probe 1 securely to the cart, and set up the cart, track, pulley, string, and force probes.

18 L6-18 Lab 6 Gravitational and Passive Forces 2. The experiment file L Tension Forces is also appropriate for this activity. You will have graphs of the two force probes versus time. 3. Zero both force probes with the string loose. Hold the cart to keep it from moving. Then begin graphing while pulling on force probe 2. Pull softly at first, then harder, and then alternately soft and hard. Do not exceed 10 N. 4. Print out one set of graphs for your group report. Question 4-2: Based on your observations of the readings of the two force probes, was the pull you exerted on force probe 2 transmitted undiminished to force probe 1 even though it went through a right angle bend? How does this compare to your prediction? Discuss. Activity 4-3: Tension and Newton s Second Law Prediction 4-3: Suppose that in place of force probe 2 you hang a 50 g mass from the end of the string. With the cart held at rest, what value do you expect force probe 1 to read? Be quantitative. Explain. Prediction 4-4: Suppose that you hang the same 50 g mass but release the cart and let it accelerate as the mass falls. Do you expect force probe 1 to read the same force or a larger or smaller force as the cart accelerates? Explain.

19 Lab 6 Gravitational and Passive Forces L6-19 To test your predictions you will need the following in addition to the equipment for Activity 4-2: 50 g mass 1. Use the same setup as for Activity 4-2, but replace force probe 2 with a hanging mass and set up the motion detector. 2. Determine the mass of the cart and force probe: g 3. Open the experiment file called L Tension and N2. 4. Be sure that the motion detector can see the cart all the way to the end of the track. 5. Hang the 50 g mass from the end of the string, and hold the cart at rest at least 20 cm away from the motion detector. 6. Just before you are ready to start zero the force probe with the string loose. Let the 50 g mass hang without swinging and then begin graphing. Hold the cart for the first second after you hear the clicks of the motion detector and then release it. Be sure to stop the cart before it comes to the end of the track. 7. Print out one set of graphs for your group. Use arrows on your force and acceleration graphs to indicate the time when the cart was released. 8. Use the statistics or linear fit features of the software to measure the average value of the tension measured by the force probe before the cart was released and while it was accelerating. Also measure the average value of the acceleration during the time interval while the cart had a fairly constant acceleration. Average tension with cart at rest: ± N Average tension with cart accelerating: ± N Average acceleration: ± m/s 2 Question 4-3: How did the tension while the cart was at rest compare to the weight of the hanging mass? [Hint: Remember that weight mg.] Did this agree with your prediction? Was the force applied to the end of the string by the hanging mass transmitted undiminished to the cart, as you observed in the previous activity? Question 4-4: Did anything happen to the tension after the cart was released? How did the value of the tension as the cart was accelerating compare to the weight of the hanging mass? Did this agree with your prediction? Discuss.

20 L6-20 Lab 6 Gravitational and Passive Forces Comment: When the cart is released, both the cart and hanging mass must always move with the same velocity since they are connected by the string as a single system. Thus, the cart and mass must have the same acceleration. According to Newton s second law, the combined (net) force on the cart must equal its mass times the acceleration, and the combined (net) force on the hanging mass must equal its mass times the same acceleration. Question 4-5: Use Newton s second law to explain your answer to Question 4-4. Why must the tension in the string be smaller than the weight of the hanging mass if the hanging mass is to accelerate downward? Please clean up your lab area