unit 5: force and motion - simon fraser university · 2015. 9. 24. · workshop physics ii: unit 5...

Name ________________________ Date (YY/MM/DD) ______/_________/_______

SFU e-mail. [email protected] Section_______ Group________

UNIT 5: FORCE AND MOTIONApproximate Classroom Time: Two 100 minute sessions

A vulgar Mechanik can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest til he gets over every rub.

Isaac Newton (1694)

OBJECTIVES

• To develop the concept of force in terms of how it is measured

• To learn how to use a force probe to measure force

• To understand the relationship between forces applied to an object and its motions

• To find a mathematical relationship between the force applied to an object and its acceleration

OVERVIEW15

In the previous labs you have used a motion detector to display position-time, velocity-time and acceleration-time graphs of the motion of different objects. You were not concerned about how you got the objects to move, i.e., what forces (pushes or pulls) acted on the objects. From your experi-ences, you know that force and motion are related in some way. To start your bicycle moving, you must apply a force to the pedal. To start up your car, you must step on the gas pedal to get the engine to apply a force to the road through the tires.But, exactly how is force related to the quantities you used in the previous unit to describe motion--position, velocity and acceleration? In this unit you will pay attention to forces and how they affect motion. You will first develop an operational idea of a force as a push or a pull. You will learn how to measure forces. Then you will apply forces to a cart, and observe the nature of its resulting motion graphically with a motion detector.

Neil Alberding, Simon Fraser University, Physics Dept. Portions ©1990-93 Dept. of Physics and Astron-omy, Dickinson College Supported by FIPSE (U.S. Dept. of Ed.) and NSF.

SESSION ONE: MEASURING FORCES AND RELATING FORCE TO MOTION

10 minHow large is a pull?In this investigation you will explore the concept of a con-stant force and the combination of forces in one dimension. You can use these concepts to learn how to measure forces with a force probe. You will need the following materials:• Logger Pro software• RealTime Physics Mechanics Experiments folder• Force probe• LabPro Interface • Three identical rubber bands• Metre stick• Spring scale (2, 5 or 10 N maximum reading)

✍ Activity 5-1: Creating and Measuring ForceIf you pull on a rubber band attached at one end, you know it will stretch. The more you pull, the more it stretches. To measure the force we can use a calibrated spring scale. (a) Attach one end of the rubber band to something on the table

that can't move. Also attach the metre stick to the table. Now stretch the rubber band so it is several centimetres longer than its relaxed length. Does it always seem to exert the same pull on you each time it is stretched to the same length? (Most people agree that this is obvious.)

(b) Write down the length you have chosen in the box. This will be your standard length for future measurements.

(c) Now find a spring scale which you think would be able to measure the force of the rubber band when stretched at your standard length. Hold the scale with nothing attached to it and verify that it reads Zero newtons. If not, then turn the adjustment screw at the top until it reads Zero.

(d) Hook the rubber band onto the spring scale and pull it to your Standard Length. Read the force created by the rubber band in newtons.

(e) Attach the ends of two identical rubber bands in the same way as before and stretch them both to the standard length. What force is measured now? Repeat for three rubber bands. Enter the data in the table.

Question: Is the net force proportional to the number of rubber bands used in parallel? Use the data in the table to determine the force per rubber band when stretched at the standard length.

Page 5-2 Workshop Physics Activity Guide SFU 1157

Neil Alberding, Simon Fraser University, Physics Dept., 2008. Portions ©1990-93 Dept. of Physics and Astronomy, Dickinson College Supported by FIPSE (U.S. Dept. of Ed.) and NSF.

Record the standard length of the rubber band:

_________________ cm

# of rubber bands

Force (N)

1

2

3

Question: Suppose you stretched a rubber band by pulling on it to your standard length. Now you want to create a force ten times as large. One of your lab partners suggests to stretch the rubber band at ten times the standard length. Would you agree? Why or why not? If not, suggest a better way.

Question: Suppose you applied a force with a stretched rubber band one day, and several days later you wanted to feel the same force or ap-ply it to something. How could you assure that the forces were the same? Explain.

The Force Probe

The standard unit of force is called the newton, abbrevi-ated N and will be precisely defined later in this unit. For the rest of your work on forces and the motions they cause, it will be more convenient to use the electronic force probe that reads in newtons. The spring scale has already been calibrated in newtons. Since the properties of the springs don’t change much with time we don’t usually need to re-calibrate a spring scale before use. An electronic force probe needs to be recalibrated from time to time because its characteristics are less stable than those of a simple spring scale. To calibrate the force probe to read forces in newtons just use the spring scale to input two standard force measurements. Furthermore, like a spring scale, a force probe needs to be zeroed before making a series of measurements. Once calibrated and zeroed, the force probe will be very useful in our study of force and motion.

✍ Activity 5-2: Calibrating a Force ProbeBefore using the force probe for serious work it is necessary to calibrate it against a known standard. (OK, so you may question the reliability of our cheap plastic spring scales, but they are calibrated and they’re the best we’ve got!) This cali-bration procedure assumes that the force probe’s response to force is linear. If both the spring scale and force probe are zeroed before use, then the relationship is “proportional.”

Workshop Physics II: Unit 5 — Force and Motion Page 5-3 SFU 1157


(a) Set up the force probe by plugging it into analog port 1 of the LabPro. Push the switch to the ±50 N position. Turn on the LabPro, and open the LoggerPro software. The hook should be screwed into the active end of the force probe.

(b) Pull gently on the hook of the force probe and make sure the force reading changes on the computer screen.

(c) Since the electronic signal from the force probe can change slightly from time to time as the temperature changes, it is always a good idea to Zero the force probe right before taking measurements. Zero the force probe.

(d) To calibrate the force probe, select “Calibrate Force” from the Experiment menu, then Calibrate Now, and follow the direc-tions exactly.

When the computer asks you to apply a known force to the force probe, pull on the hook with the spring scale, holding it with a steady 10.0 N reading on the scale. Enter this value in the space, continue to hold a steady reading, and press keep.

You then need to enter a second value. Pull the spring scale to 20.0 N. hold it steady and press keep again. You can now exit the calibration screen.

(e) Check the calibration. First Zero the force probe. Then Start recording data, and pull on the force probe with the spring scale with several different forces, all 50.0 N or smaller. Use Examine to record the force probe readings and corresponding spring scale readings in the table below.

Question: Do your force probe readings correspond to your spring scale readings? Can you now use the force probe to make reasonably accurate force measurements?

Relationship between Force and MotionNow you can use the force probe to apply measured amounts of force to an object. You can also use the motion detector, as in the previous three units, to examine the mo-tion of the object. In this way you will be able to establish the relationship between motion and force.You will need the following materials:

• Logger Pro software

• RealTime Physics Mechanics Experiments folder

• Force probe



Force probereading (N)

Spring scalereading (N)

• Motion detector

• Lab Pro interface

• Spring scale (2, 5, 10 or 20 N maximum reading)

• Cart or toy car with very little friction

• Smooth track

• Low friction clamp-on pulley, light weight string, variety of hanging masses

✍ Activity 5-3: Pushing and Pulling a CartIn this activity you will move a cart by pushing and pulling it with your hand. You will measure the force, velocity and acceleration. Then you will be able to look for relationships between the applied force and the motion quantities, to see which is (are) related to force.

(a) Set up the cart, force probe and motion detector on a smooth level surface as shown below. The cart should have a mass of about 1 kg with force probe included. Fasten additional mass to the top if necessary. The force probe should be fastened securely to the cart and plugged into analog port 1 of the LabPro. The mo-tion detector should be plugged into port 2. (Be sure that the cable from the force probe will not be seen by the motion detector.)

0.3m

Prediction: Suppose you grasp the force probe hook and move the cart forwards and backwards 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 motion quantities related to force? That is to say, if you apply a changing force to the cart, will the velocity or accel-eration change in the same way as the force?

(b) To test your predictions, open the experiment file called L03A2-1 (Motion and Force). This will set up veloc-ity, force and acceleration axes with a convenient time scale of 5 seconds, as shown below. Check that a 2 N



pull from the spring scale gives about 2 N reading on the graph. Zero the force probe.

Time (seconds)1 2 3 4 50

–2

0

2

Velo

city (

m/s

)

1 2 3 4 50–2

1

2

Fo

rce (

N)

Time (seconds)


–2

0

2

Accele

ration (

m/s

/s)

(c) Grasp the force probe hook and press Collect. When you hear the clicks, pull the cart away from the motion detector, and quickly stop it. Then push it back to-wards the motion detector, and again quickly stop it. Be sure that the cart never gets closer than 0.2 m away from the detector.

(d) Sketch your graphs on the axes above.

Question: Does either graph-velocity or acceleration-resemble the force graph? Which one? Explain.



Question: Based on your observations, does it appear that either the velocity or acceleration of the cart might be related to the applied force? Explain.

✍ Activity 5-4: Speeding Up You have seen in the previous activity that force and accel-eration seem to be related. But just what is the relation-ship between force and acceleration?

Prediction: Suppose you have a cart with very little friction, and that you pull this cart with a constant force as shown below on the force-time graph. Sketch on the axes below the velocity-time and acceleration-time graphs of the cart's motion.

PREDICTION +

–+

–+

–

0

0

0

Force

Velocity

Acceleration

Describe in words the predicted shape of the velocity vs. time and accel-eration vs. time graphs for this cart which you sketched.

(e) Test your predictions. Set up the ramp, pulley, cart, string, motion detector and force probe as shown below.



0.3m

Be sure that the cart's friction is minimum. (If the cart has a friction pad, it should be raised so it doesn't con-tact the ramp.)

(f) Prepare to graph velocity, acceleration and force. Open the experiment called L03A2-2 (Speeding Up) to dis-play the velocity, acceleration and force axes shown on the next page.

(g) It is important to choose the amount of the falling mass so the cart doesn't move so fast that you can't observe the motion. Experiment with different hanging masses until it takes at least one second for the cart to reach the end of the track after the mass is released. Also test to be sure that the motion detector sees the cart during its complete motion. Remember that the back of the cart must always be at least 0.2 metre from the motion detector.

(h) Calibrate the force probe with a force of 2.0 N applied to it with the spring scale if you haven't already done so.

(i) Zero the force probe with the string hanging loosely so that no force is applied to the probe. Zero it again be-fore each graph.

(j) Single click on the velocity graph to graph velocity first. Start graphing by pressing Collect. Release the cart after you hear the clicks of the motion detector. Be sure that the cable from the force probe is not seen by the mo-tion detector, and that it doesn't drag the cart. Repeat until you get good graphs in which the cart is seen by the motion detector over its whole motion.

(k) Choose “Store Latest Run” under the Experiment menu to keep the data for comparison in the next activ-ity.



Record the hanging mass that you decided to use:

_____________________

! ! ! FINAL RESULTS

!


–2

0

2

Velo

city (

m/s

)


–2

0

2

Accele

ration (

m/s

/s)

1 2 3 4 500

1

2

Fo

rce (

N)

Time (seconds)

(l) If necessary, adjust the axes to display the graphs more clearly. Sketch the actual velocity, acceleration and force graphs on the axes above. Draw smooth graphs; don't worry about small bumps.

Question: Is the force which is applied to the cart by the string con-stant, increasing or decreasing? Explain based on your graph.



Question: How does the acceleration graph vary in time? Does this agree with your prediction? What kind of acceleration corresponds to a constant applied force?

Question: How does the velocity graph vary in time? Does this agree with your prediction? What kind of velocity corresponds to a constant applied force?

✍ Activity 5-5: Acceleration from Different ForcesIn the previous activity you have examined the motion of a cart with a constant force applied to it. But, what is the relationship between acceleration and force? If you apply a larger force to the same cart (same mass as before) how will the acceleration change? In this activity you will try to answer these questions by applying different forces to the cart and measuring the corresponding accelerations.

Prediction: Suppose you pulled the cart with a force about twice as large as before. What would happen to the acceleration of the cart? Ex-plain.

(a) Test your prediction. Keep the graphs from the previ-ous activity.

(b) Accelerate the cart with a larger force than before. To produce a larger force, hang a mass about twice the mass as in the previous activity.

(c) Graph force, velocity and acceleration as before. Don't forget to Zero the force probe with nothing attached to the hook right before graphing.



Record the 2nd hanging mass that you decided to use:

_______________________

(d) Sketch your graphs as well as the stored graphs on the axes below.

FINAL RESULTS


–2

0

2

Velo

city (

m/s

)


–2

0

2

Accele

ration (

m/s

/s)

1 2 3 4 500

1

2

Fo

rce (

N)

Time (seconds)

(e) Measure the average force and average acceleration for the cart for this activity and the previous activity, and record your measured values in the table on the top of the next page. Find the mean values only during the time intervals when the force and acceleration are nearly constant. (Select Examine from the Analyze menu. Click with the cursor on the force graph at the beginning of the time interval over which you want to find the mean force, and--while holding down the mouse button-- slide



the cursor across to the end of the interval. This se-lected region on the graph should darken.

Release the mouse, and then select Statistics . . . from the Analyze menu. The mean values of acceleration and force will be displayed.)

! !

Average Force (N)

AverageAcceleration

(m/s2)

Activity 5-4

Activity 5-5

Activity 5-6

Question: How did the force applied to the cart compare to that with the smaller force in the previous Activity?

Question: How did the acceleration of the cart compare to that caused by the smaller force in the previous Activity? Did this agree with your prediction? Explain.

✍ Activity 5-6: The Relationship Between Accel-eration and Force.If you accelerate the same cart (same mass) with another force, you will then have three data points--enough data to plot a graph of acceleration vs. force. You can then find the mathematical relationship between acceleration and force.(a) Accelerate the cart with a force roughly midway be-

tween the other two forces tried. Use a hanging mass about midway between those used in the last two ac-tivities and record the mass.

(b) Graph velocity, acceleration and force. Sketch the graphs on the axes that you used before.

(c) Find the mean acceleration and force, as before, and record the values in the table.



Record the 3rd hanging mass that you decided to use:

_______________________

(d) Plot a graph of acceleration vs. force from the data in the table. Plot the data by hand on the axes provided and label the scales properly.

Average Force (N)

Avera

ge A

ccele

ration (

m/s

2)

(e) Determine the mathematical relationship between the acceleration of the cart and the force applied to the cart as displayed on your graph.

Question: Does there appear to be a simple mathematical relationship between the acceleration of a cart (with fixed mass) and the force applied to the cart (measured by the force probe mounted on the cart)? Write down the equation you found and describe the mathematical relation-ship in words.

Question If you increased the force applied to the cart by a factor of ten, how would you expect the acceleration to change? How would you expect the acceleration-time graph of the cart's motion to change? Ex-plain based on your graphs.



Question: If you increased the force applied to the cart by a factor of ten, how would you expect the velocity-time graph of the cart's motion to change? Explain based on your graphs.



SESSION TWO: FORCE MASS AND ACCELERATIONYou have seen that the acceleration of an object is directly proportional to the combined or net force acting on the ob-ject. If the combined force is not zero, then the object will accelerate. If the combined force is constant, then the ac-celeration is also constant. These observations are part of Newton's Second Law of Motion. You have also seen that for an object to move at a constant velocity (zero acceleration) when friction is negligible, the combined or net force on the object should be zero. The law which describes constant velocity motion of an object is Newton's First Law of Motion. Newton's First and Second Laws of Motion are very powerful! They allow you to re-late the force on an object to its subsequent motion. There-fore, when the nature of the force(s) acting on an object is known, then Newton's laws of motion allow you to make mathematical predictions of the object's motion. In Activity 5-7 you will study how the amount of "stuff" (mass) you are accelerating with a force affects the magni-tude of the acceleration. What if the mass of the object were larger or smaller? How would this affect the accel-eration of the object for a given combined force? In Activity 5-8 you will study more carefully the definitions of the units in which we express force, mass and accelera-tion.

Measuring MassIn previous activities you have applied forces to a cart and examined its motion. Up until now, you have always used a cart with the same mass. But when you apply a force to an object, you know that its mass has a large effect on the object's acceleration. For example, compare the different accelerations that would result if you pushed a 1000 kilo-gram (metric ton) automobile and a 1 kilogram cart, both with the same size force!It would be nice to be able to do a mechanics experiment in one part of the world and have scientists in another part of the world be able to replicate it or at least understand what actually happened. This requires that people agree on standard units. In 1960 an international commission met to agree upon units for fundamental quantities such as length, time, mass, force, electric current, pressure, etc. This commission agreed that the most fundamental units in the study of mechanics are length, time, and mass. All other units including force, work, energy, torque, rota-tional velocity, etc. which you encounter in your study of mechanics can be expressed as a combination of these basic



quantities. The fundamental International System or SI (Système Internationale) units along with the standard unit for force are shown below.

FUNDAMENTAL UNITS FOR MECHANICS

Length: A metre (m) is the distance travelled by light in a vacuum during a time of 1/299,792,458 second.

Time: A second (s) is defined as the time required for a cesium-133 atom to undergo 9,192,631,770 vibrations.

Mass: A kilogram (kg) is defined as the mass of a platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in Sèvres France. It is kept in a special chamber to prevent corrosion.

Suppose you want to find the mass of an object in kilo-grams. You need to compare it to the one kilogram platinum-iridium alloy cylinder at the International Bu-reau of Weights and Measures in France. It would be nice to have a standard kilogram in your laboratory. You could go to France, but it is unlikely that they would let you take the standard home with you!Suppose, however, that you accelerate the standard mass with a constant force and measure the force and also the resulting acceleration as accurately as possible. Next you would need to make a cylinder that seemed just like the standard one and add or subtract stuff from it until it un-dergoes exactly the same acceleration with the same con-stant force. Then within the limits of experimental uncer-tainty this new cylinder standard and the bureau standard would have the same mass. If the comparison could be made to three significant figures, then the mass of your new standard would be mstd = 1.00 kg.Suppose you head home with your standard mass. You wish to determine the mass of another object. You could apply the same constant force, F, on the standard and on the other object, and measure both accelerations. Then, according to Newton's Second Law, F = ma,

m_{\rm std} = 1.00 {\rm ~ kg}= \frac{F}{a}m_{\rm other} = \frac{F}{a_{\rm other}}

mstd = 1.00 kg =

F

a mother =

F

aother



Since the constant force, F, applied to both masses was the same,

m_{\rm other} = 1.00 {\rm ~kg}\frac{a}{a_{\rm other}}mother = 1.00 kg

a

aotherIn this Activity you will explore the mathematical relation-ship between acceleration and mass when you apply the same constant force to a cart while changing the mass.You will need:

• Lab Pro software


• Motion detector

• Lab Pro interface

• Low-friction cart

• “standard” bar mass, 0.25 kg

• Force and Motion track

• Fan accessory + four batteries. Two dummy batteries in their holders

• Variety of additional masses (e.g., tennis ball, steel ball)

✍ Activity 5-7: Acceleration and MassYou can easily change the mass of the cart by attaching masses to it, and you can apply the same force to the cart by using the fan accessory. By measuring the acceleration of different mass carts, you can find a mathematical relation-ship between the acceleration of the cart and its mass, with the applied force kept constant.

(a) Set up the track, cart, fan, motion detector. Be sure that the track is level. Use the fan accessory with all the batteries in-stalled

The motion detector should be plugged into DIG/SONIC 1 and use any setup file that measures velocity vs time such as L03A2-1(Motion and Force).cmbl.

(b) First measure the acceleration of the cart and fan without any additional mass.1

Record the velocity vs. time graph,

Select a region of the graph after release and before crash and that is relatively linear.

Choose “Linear Fit”. The acceleration is the slope of the graph



1 Two possible sources of systematic error in the acceleration measurement are friction and the track not being level. These can be reduced by careful experimental technique. See the Challenge for hints on dealing with friction.

acceleration of cart+fan = ________________________

Copy this number to the appropriate cell of the table.

(c) Place the mass bar on the cart, under the fan, and again measure the acceleration, as before, with the additional mass

acceleration of cart+fan+bar __________________

Copy this number to the appropriate cell of the table.

(d) Calculate the mass of the cart+fan in terms of the standard bar mass and enter the mass into the mass cell in the first row.

Use the relationship m1/m2 = a2/a1. In this way we are using inertia as a way of measuring mass.

mass of cart+fan = ____________________ bars

(e) Assume that the bar mass is calibrated to be exactly 0.250 kg. Determine the mass of the cart+fan in kg.

mass of cart+fan = ____________________ kg

Prediction: Suppose that you place another standard bar on the cart, and accelerate it with the same applied force. Predict the acceleration and enter the predicted value after the “pred:” in the table.

(f) Test your prediction. Place another bar on the cart (borrow-ing one from a neighbour if necessary) and measure the accel-eration. Enter the measured value in the table after “meas:” and compare the value with your prediction.



Comment: Physicists call the quantity you have just calculat-ed—the ratio of combined (net) force on an object to its acceleration—the inertial mass of the object.

Question: Did the acceleration agree with your prediction? If it’s different, is it significantly different? (That is, considering the accuracy of your measurement, is any difference between the pre-dicted value and the measured value real and reproducible?)

Explain

(g) Take off the extra bar and place another object that will fit on the cart and cause a significant increase in the total mass. Measure the acceleration again and determine the mass of the extra object that you just put on the cart. For next week’s activities you will need to know the inertial masses of a tennis ball and a steel ball. You can measure both of these masses now.

Measuring ForceSo far you have been measuring force in standard units based on the pull exerted by a spring scale calibrated in newtons. Where does this unit come from? We need a way to define the unit of force without having a spring scale that is already calibrated. That can be done if we ac-cept the relation

F = maWe know how to measure acceleration by observing the motion of an object. The mass of something is measured by comparing accelerations when the same force is exerted on it and on a standard mass. The unit of force called a new-ton is that amount of force that would accelerate one kilo-gram one m/s2.In the following experiment we shall find the force that the fan exerts on the cart by measuring the acceleration of known masses. You will need the following equipment:

• Logger Pro software


• Motion detector

• LabPro interface

• Spring scale with a maximum reading of 5 N



After you measure the iner-tial masses of the tennis ball and the steel ball, copy them into the next unit’s activity guide.

• Plastic bag with handle

• Low friction cart

• Fan Accessory

• Force and Motion Track

✍ Activity 5-8: Calculating the Fan Force in Newtons

(a) You have already enough data to calculate the force of the fan cart when it has four batteries. Use Newton’s second law to calculate the force exerted by the fan cart.

Calculate the Fan force in each case and enter the values in the table. Comment on whether the values are consistent with each other or not. If you don‘t think they are consistent, why?

Question: Each of the forces calculated was the result of the fan accessory and four batteries. There are probably differences in the calculated values obtained, even though the force was expected to be the same. Comment on whether you think any differences are due to random experimental errors, or whether the differences represent real variations of the force.

You could continue to determine and compare masses by ac-celerating them and taking force to acceleration ratios, but this process is pretty tedious.

A simpler approach is to use a spring scale to compare the weights of the object of unknown mass with the standard mass. Spring scales measure weight in newtons, but are often calibrated in kilograms. This is possible because gravita-tional forces at a given location are proportional to mass.

(b) Compare your inertial mass measurement of the cart+fan with its weight that you measure by placing them in a plastic bag and measuring with a spring scale and record under the “weight” column in the table. Do the same for cart+fan+bar.

Question: The ratio weight/(inertial mass) is called the gravitational field strength, g. Calculate g from your data.



THE FORCE UNIT EXPRESSED IN TERMS OF

LENGTH, MASS, AND TIME

Force: A newton (N) is defined as that force which causes a 1 kg mass to acceler-

ate at 1 m/s2 .

Question: If you change the number of batteries and place an object of unknown mass in the cart, can you determine either the value of the force in newtons or the value of the mass in kilo-grams?

Comment: In your experiments, you have seen that the physical quantities force, mass and acceleration are related through Newton's Second Law. In the activity you have just done, you have used this relationship to define force in terms of standard units of mass, length and time. This is a good logical definition of inertial mass. It would also be possible to use standard units of force, length and time and then define mass.

Question: What would be the units of mass if the standard units were newtons, metres and seconds?

✍ Activity 5-9: Determine the force of the fan cart with fewer than four batteries.

(a) Set up the track, cart, fan accessory, and motion detector.

Place known masses on the cart and replace two batteries with the dummy slugs. Place the unused batteries in the holders where the slugs were.

(b) Measure the acceleration produced by the fan in this case. Fill in the next row in the table and calculate the force.

(c) Change the mass and repeat step b and fill in the next row.

(d) If you have time you can also measure the force produced by using three batteries or even one single battery.



Question: Do you think that the relationship between number of batteries and the force is linear?

Question: A force of 5.4 N is applied to an object, and the object is observed to accelerate with an acceleration of 3.0 m/s2.. If fric-tion is so small that it can be ignored, what is the mass of the ob-ject in kg? Show your calculation.

Question: An object of mass 39 kg is observed to accelerate with an acceleration of 2.0 m/s2. If friction is negligible, what is the force applied to the object in N? Show your calculation.

Comment: The main purpose of this unit has been to ex-plore the relationship between the forces on an object, the object's mass, and its acceleration. You have been trying to develop Newton's First and Second Laws of Motion for one-dimensional situations in which all forces lie in a positive or negative direction along the same line. ! !



✍ Activity 5-10: Newton's Laws in Your Own Words

Question: Express Newton's First Law (the one about constant velocity) in terms of the combined (net) force applied to an object in your own words clearly and precisely.

Question: Express Newton's First Law in equations in terms of the acceleration vector, the combined (net) force vector applied to an object, and its mass.

If

€

! F ∑ = then

€

! a = and

€

! v =

Question: Express Newton's Second Law (the one relating force, mass, and acceleration) in terms of the combined (net) force ap-plied to an object in your own words clearly and precisely.

Question: Express Newton's Second Law in equations in terms of the acceleration vector, the combined (net) force vector applied to an object, and its mass.

If

€

! F ∑ ≠ 0 then

€

! a =

Comment: The use of the equal sign does not signify that an acceleration is the same as or equivalent to a force di-vided by a mass, but instead it spells out a procedure for calculating the magnitude and direction of the acceleration of a mass while it is experiencing a net force. What we as-sume when we subscribe to Newton's Second Law is that a net force on a mass causes an acceleration of that mass.



Beware, the equal sign has several different meanings in text books and even in these labs. In order to reduce con-fusion a few of the meanings of and symbols used for the "equal" sign are summarized below:

= the same as (e.g., 2+2 = 4)= also means equivalent to (e.g., four quarters is equivalent

in buying power to one dollar)= can be calculated by (e.g., in physics for a body undergoing

constant acceleration v = vo + at)

= is replaced as (e.g., in a computer program x= x+1 means replace x with the value x+l)

≈ , ~ is approximately the same as or equivalent to≡ is defined as (e.g., vavg ≡ (x2-x1)/(t2-t1))

FINAL COMMENTS ON FORCE MASS AND ACCELERATIONYou started your study of Newtonian Dynamics in Unit 5-1 by attempting to develop the concept of force. Initially when asked to define forces most people think of a force as an obvious push or pull such as a punch to the jaw or the tug of a rubber 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 seem to be the same at all. Pulling on a hook attached to 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 as that which causes accelera-tion and that if the obvious applied forces did not account for the degree of acceleration then other "invisible" forces must be present. A prime example of an invisible force is the gravitational force--the attraction of the earth for ob-jects. Finding invisible forces is often hard because some of them are not active forces. Rather, they are passive forces which come up in response to active ones. They are not only in-visible, but they only crop up to oppose active forces.



Friction is an invisible passive force. The passive nature of friction is obvious when you think of an object like a block being pulled along a rough surface at constant velocity. There is an applied force (active) in one direction and a friction force in the other direction which opposes the mo-tion. If the applied force is discontinued the block will slow down to rest but it will not start moving in the oppo-site direction due to friction. This is because the friction force is passive and stops acting as soon as the block comes to rest.

CHALLENGE: Dealing with FrictionIn your attempts to measure mass using the fan cart you probably noticed that the Inertial Mass measurement with the fan cart differed from the Gravitational Mass as meas-ured by the scale. Later we will study friction and find that the strength of the frictional force increases with the weight of the object. Furthermore the force is always oppo-site the direction of motion. The direction of the fan’s force is always in the same direction.Speculate on how our neglect of frictional forces could have affected the inertial mass measurement. Would it have made the measurement too low or too high? Does it depend on whether the fan is causing the cart to speed up or slow down? How can the experiment be done so that the effect of friction is reduced or eliminated?



Force, Mass and Acceleration TableSource of

forceObject Acceleration

(m/s2)Inertial

Mass (kg)Force (N)

of fan

Weight (N)

of object

fan & 4 batteries

cart+fan

fan & 4 batteries

cart+fan + ¼kg bar

fan & 4 batteries

cart+fan + 2 ¼kg bars

pred: meas:

fan & 4 batteries

cart+fan +_________

fan & __ batteries

cart+fan +_________

fan & __ batteries

cart+fan +_________

fan & __ batteries

cart+fan +_________

fan & __ batteries

cart+fan +_________

fan & __ batteries

cart+fan +_________



unit 5: force and motion - simon fraser university · 2015. 9. 24. · workshop physics ii: unit 5...

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