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M o d e l N o . M E - 9 5 0 2

E x p . 1 1 B : M i n i m u m P e r i o d o f a P h y s i c a l P e n d u l u m

0 1 2 - 1 2 8 7 6 B

Exp. 11B: Minimum Period of a Physical Pendulum

Equipment Needed

Theory

The period of oscillation for a physical pendulum can be written as
follows:

where

is the moment of inertia (rotational inertia) for the physical

pendulum,

is the perpendicular distance from the axis at the pivot

point to the parallel axis at the center of mass,

, and

is the mass

of the pendulum.

The moment of inertia,

, for a rectangular-type rod about its center

of mass is:

where

is the length and

is the thickness of the rectangular-type

rod. However, if the length,

, is much greater than the thickness,

then the following can be used as a very good approximation of the
moment of inertia around the center of mass:

where

is the mass and

is the length of the rod.

If the rod pivots around any other axis that is parallel to the axis through the center of mass, the Parallel Axis The-
orem states that the moment of inertia about the parallel axis,

parallel

, is the sum of the moment of inertia around

the center of mass,

, plus

, where

is the mass of the rod and

is the perpendicular distance from the

center of mass to the pivot point, or

The formula for the period of oscillation becomes

At what distance,

, does the period of oscillation,

, become a

minimum

In this experiment you will determine the distance,

, from the pivot point to the center of mass that gives the

minimum period of oscillation for the physical pendulum.

Item

Statics Board

Balance Arm

Stopwatch (ME-1234)

Figure 11.5: Physical Pendulum



mg sin



mg cos



Equilibrium

position

Pivot
point

Center of

mass



-----------------

------

m a





------

parallel

------



------

-------------------------------

Содержание ME-9502

Страница 1: ... PASCO Mechanics Statics System ME 9502 Instruction Manual 012 12876B 012 12876 ...

Страница 2: ...with a PASCO Mass Hanger from the ME 8979 Mass and Hanger Set suspended by a thread over a Small Pulley Most of the components of the Statics System are held magnetically to the included workboard This manual contains fifteen copy ready experi ments about the fundamentals of statics ...

Страница 3: ...f Physical Bodies 29 6 Torque Non Parallel Forces 33 7 The Inclined Plane 37 8 Sliding Friction and Static Friction 41 9 Simple Harmonic Motion Mass on a Spring 47 10 Simple Harmonic Motion The Simple Pendulum 53 11A Simple Harmonic Motion Physical Pendulum 57 11B Minimum Period for a Physical Pendulum 63 11C Simple Harmonic Motion Beam on a Spring 67 12 Simple Machines The Lever 73 13 Simple Mach...

Страница 4: ... Statics System iv 012 12876B ...

Страница 5: ...hich forces can be applied to an object without causing acceleration The second reason is that in our everyday experience non accelerated systems are the rule not the exception Equipment The ME 9502 Statics System consists of the Statics Board Spares Package Components Package and Mass and Hanger Set ME 9503 Statics Board The Statics Board is a ferrous metal plate approximately 45 by 45 centimeter...

Страница 6: ...ailable sepa rately can be attached to the first board with the three included con nector screws To join the boards remove the connector screws from the threaded holes on the side of the first board Put the edge of the second board next to the first board Align the holes and join the two boards with the connector screws No No Yes Yes Moving Components on the Board Rear view of Statics Boards Conne...

Страница 7: ...ASCO load cells load cell amplifiers interfaces hand held data loggers and data acquisition software Item Qty Item Qty String Tie Assembly 3 Thumbscrew 6 32 by 5 8 for Cord Clip 2 Torque Indicator Assembly 6 Thumbscrew 4 40 by 1 2 for balance arm protractor 2 Nylon Thread spool 1 Thumbscrew 6 32 by 1 4 for balance arm pivot 1 Cord Tensioning Clip 2 Washer 0 285 OD for balance arm protractor 2 Angl...

Страница 8: ... the Angle Indicator Arms thumbscrews washers and brass weight are replacement parts String Tie Assembly When the String Tie Assembly is snapped into the center of the Force Wheel Assembly you can use the apparatus to study force vectors The String Tie Assembly has two parts a clear plastic inner part the force disk that is free to move around in the center of the outer part which has a center hol...

Страница 9: ...eys and one Large Pulley mounted on magnetic bases It also includes a Double Pulley Block that does not have a magnetic base The Double Pulley Block is designed for block and tackle experiments A support thread can be tied to either end of the Double Pulley Block All the pulleys have low friction ball bearings The smaller pulleys are 2 41 cm 0 850 outside diameter OD and 1 65 cm 0 650 inside diame...

Страница 10: ...ob The ME 9504 Spares package includes a spare plumb bob brass weight To replace the plumb bob use a Phillips head crosshead screwdriver to loosen the screw on the back of the degree scale Remove the piece of thread and get a new piece approximately 10 cm 4 long Put one end of the thread through the hole in the brass weight and tie a double knot in that end of the thread so it will not slip back t...

Страница 11: ...e wheel will stay in position until moved again REMINDER Be sure to put tie three threads through the hole in the center of the String Tie before putting the String Tie into the Force Wheel The String Tie Assembly snaps into the hole in the center of the Force Wheel Assembly Align the tabs on the String Tie with the notches inside the hole at the center of the Force Wheel Push the String Tie firml...

Страница 12: ...the center of the protractor and sliding the protractor along the beam Note that not all experiments need three protractors Reading the Scale Read the position of the protractor relative to the midpoint through the two rectangular windows on the protractor The bottom window shows the position to the nearest centimeter and the top window shows the position to the millimeter The top window has a sma...

Страница 13: ... thread to a Load Cell see above that is mounted on the Utility Mount It is best to attach the thread through the clip before the clip is installed on the mount or on a Load Cell The Cord Clip has two parts but it does not come apart Start by holding the top part of the clip so the two parts are separate as shown in Figure A leaving an opening through which the thread can be threaded Insert the th...

Страница 14: ... forces torques and center of mass are explored Advanced Experiments allow the student to combine the principles already studied to understand such phenom ena as static equilibrium Friction and simple harmonic motion are also investigated Simple Machines provide an opportunity for the student to investigate applications of the principles already stud ied and also to introduce important new concept...

Страница 15: ...nt k The constant is called the spring constant Setup Place the Spring Scale on the Statics Board so that the spring hangs ver tically in the tube Do not hang anything on the bottom hook The indi cator must be aligned with the zero mark on the label To zero the Spring Scale loosen the thumbnut at the top of the scale Turn the top hook clockwise to lower the indicator and counter clockwise to raise...

Страница 16: ... meter Spring constant _____________________________ Using a Spring Scale to Measure Force Hang 160 g 0 160 kg on the Spring Scale Calculate the weight based on F mg Read the force in newtons from the Spring Scale Weight _______________ Spring Scale reading ______________ How does the measurement from the Spring Scale compare to the actual weight Calculate the percent difference Percent Difference...

Страница 17: ...is called the equilibriant FE This force has the same magnitude as the resultant FR and it has the opposite direction of the resultant Setup Set up the Spring Scale and Force Wheel on the Statics Board as shown Twist the Force Wheel until the bubble level shows that the Force Wheel is level Attach one of the threads from the force disk inner part of the String Tie in the center of the Force Wheel ...

Страница 18: ...ics Board and move the Spring Scale as shown in the figure 2 Attach threads to the bottom hook of the Spring Scale and to mass hangers over the Small Pulleys 3 Add 30 g 0 030 kg to the upper mass hanger and add 50 g 0 050 kg to the lower mass hanger 4 Adjust the Large Pulley and the Spring Scale so that the force disk is centered in the Force Wheel 5 How much can you change the mass on the hangers...

Страница 19: ...draw the resultant of F1 and F2 Label the resultant FR Measure the length of FR to determine the magnitude of the resultant force and record this magnitude on your vector diagram 3 On your diagram measure the direction of FR relative to the horizontal axis of your diagram and label the angle R Questions 1 Does the magnitude of the equilibriant force vector FE exactly balance the magnitude of the r...

Страница 20: ...Statics System Exp 2 Adding Forces Resultants and Equilibriants 16 012 12876B ...

Страница 21: ... from the force disk in the center of the Force Wheel Now pull the Spring Scale toward or away from the pulley to adjust the horizontal or x compo nent of the force Fx Adjust the amount of mass on the vertical mass hanger M2 to adjust the ver tical or y component of the force Fy Adjust the x and y components in this way until the force disk is centered in the Force Wheel Note These x and y compone...

Страница 22: ...lues are the x and y components for the resultant The magnitude of the resultant FR is the square root of the sum of the squares of the resultant s x component Rx and the y component Ry The angle of the resultant is the arctangent of the y component divided by the x component Procedure 2 Make sure that the Force Wheel is level Set up a new force F Put one thread from the force disk over a pulley a...

Страница 23: ...bination For the force disk to be in equilibrium the x components of force F1 and force F2 must be equal and opposite and the y components of F1 and F2 must add to equal the magni tude of force F3 the vertical force Set up the equipment so that the Spring Scale applies force F1 Once the sys tem is in equilibrium determine the x and y components of the vectors and compare them 3 For the setup in th...

Страница 24: ...Statics System Exp 3 Resolving Forces Components 20 012 12876B ...

Страница 25: ...f forces that cause rotation in physical bodies In doing so you will encounter a new concept torque Setup Mount the Balance Arm near the center of the Statics Board Level the Beam Loosen the thumbscrew and adjust the beam so that the zero mark on the beam is aligned with the indicator marks on the pivot When the beam is level the bubble in the bubble level will be midway between the two lines on t...

Страница 26: ... measure the total mass M1 and M2 on each side of the pivot protractor mass hanger added masses and record the masses in the data table 2 Measure the distances d1 and d2 between the centers of the protractors and the pivot and record the values in the data table 3 Take measurements for five more different values of M2 and record your results in the data table Be sure to include the units of your m...

Страница 27: ...he upward pull of the pivot point Extension If you have time try adding a third Protractor and Mass Hanger to the beam on the same side of the beam as the second Protractor Question What relationship must there be between 1 2 and 3 in order for the beam to be balanced when there are three protractors and mass hangers Case Total Mass M1 kg Weight F1 N Distance d1 m Torque 1 F1 d1 Total Mass M2 kg W...

Страница 28: ...Statics System Exp 4 Torque Parallel Forces 24 012 12876B ...

Страница 29: ...ass follows a parabolic path An object whose center of mass is above a support tends to remain in rotational equilibrium bal anced on the support In this experiment you will use your knowledge of torque to understand and locate the center of mass of an object Setup Measure and record the mass of the beam Next find the mass of two of the protractors and record the masses Note that you can use the S...

Страница 30: ...ch hanging mass is pulled down by gravity and therefore produces a torque about the pivot point of the Balance Arm 2 What is the relationship between the sum of the clockwise torques about the center of the mass and the sum of the counterclockwise torques about the center of mass Explain Add 50 grams to one mass hanger and 100 grams to the other mass hanger Loosen the thumbscrew on the beam and sl...

Страница 31: ...trical Plate that marks the position of the thread on the plate Remove the thread and mass hanger Hang the plate from a different hole Put the thread and mass hanger back on the rod Draw a new line on the plate that marks the position of the thread Repeat the process for a third different hole Draw a third line on the plate 6 Does the line showing where the thread is hanging pass through the cente...

Страница 32: ...Statics System Exp 5A Center of Mass 28 012 12876B ...

Страница 33: ...alance Arm from the Spring Scale you can now determine all the forces act ing on the Bal ance Arm As shown in the diagram these forces include F1 the weight of the mass M1 F2 the weight of the mass M2 F3 the weight of the balance beam acting through its cen ter of mass and F4 the upward pull of the Spring Scale Experiment Fill in the data table listing M in kilograms F in newtons d the distance in...

Страница 34: ... the Origin In measuring the torques the first time all the distances were measured from the point of suspension of the Bal ance Arm This measures the tendency of the beam to rotate about this point of suspension You can also measure the torques about any other point on or off the beam Using the same forces as you used before re measure the distances measuring from the left end of the balance beam...

Страница 35: ...se a pulley hanging mass and a thread to produce an additional upward force at one end of the beam You may need to use tape to secure the thread to the beam Adjust the positions of the remaining hanging masses and the Spring Scale to bring the beam back into balance so it is level horizontally Are all the forces balanced both for translational and rotations motion Diagram your setup and show your ...

Страница 36: ...Statics System Exp 5B Equilibrium of Physical Bodies 32 012 12876B ...

Страница 37: ... vector d is the distance from the pivot point to the point at which the force is applied that is the lever arm and is the angle between the force vector F and the lever arm d Note that F sin is F the component of the force vector F that is perpendicular to the lever arm d Note also that d sin is d the component of the lever arm d that is perpendicular to the force vector F In other words d sin is...

Страница 38: ...lue By moving the pulley you can adjust the angle of the force F1 Note that when you move the pulley you also need to move the Spring Scale in order to keep the thread perfectly vertical between the Spring Scale and the pulley 3 Set the angle of F1 to each of the values shown in the table below At each angle move the Spring Scale toward or away from the pulley as needed so that the magnitude of F1...

Страница 39: ...then add together the magnitudes of all the torques that tend to cause counterclockwise rotation For the system to be balanced the sum of the clockwise torques must equal the sum of the counterclockwise torques Remember that the perpendicular distance d from the pivot point to the force is equal to d sin and that the angle is measured between the lever arm d and the line of force Torque Wheel A To...

Страница 40: ...Calculate and record the torque for each force using F d Be sure to indicate whether the torque is clockwise or counterclockwise Subtract the sum of the clockwise torques from the sum of the counterclockwise torques to determine the total net torque Data Table Total Torque ________________ Question Within the limits of your experimental error is the total net torque equal to zero when the Torque W...

Страница 41: ...ne F and one parallel to the plane F The angle is the angle of inclination of the inclined plane In this experiment you will compare the mathematical solution with data taken directly from a scale model Experiment 1 Add a 100 g mass to the cart and measure and record the total mass of the cart Calculate and record the weight of the cart plus mass total mass of cart _______________ weight of cart _...

Страница 42: ... measured and calculated values divided by the average of the measured plus calculated values converted to a percentage Question How well does the calculated force based on the vector model compare to your measured force Normal Force The force that the Inclined Plane provides to support the cart is called the normal force a force perpendicular normal to the surface In the vector model of the force...

Страница 43: ...cart Arrange the pulley so the thread from the post is in line with the post and therefore is perpendicular to the plane Arrange the Spring Scale so that the angle of the thread from the pulley up to the scale is vertical Pull the Spring Scale up until the force just barely lifts the mass cart off the Inclined Plane Record the value of the Spring Scale as the perpendicular force F F measured _____...

Страница 44: ...Statics System Exp 7 The Inclined Plane 40 012 12876B ...

Страница 45: ...e is proportional to the normal force or f FN where f is the friction force and FN is the normal force The ratio of the friction force to the normal force is called the coefficient of friction The friction force is f FN The coefficient of friction is a unitless number that is between zero and one for several common surface to surface combinations and is determined empirically In this experiment yo...

Страница 46: ...rger area to the sliding friction force for a smaller area Reminders for each trial Carefully adjust the mass on the mass hanger until the weight of the hanging mass is enough so that the Fric tion Block moves at a very slow constant speed after you give it a small push Record the total mass of the Friction Block M and the hanging mass m total mass of the mass hanger and added masses Calculate and...

Страница 47: ...rallel to the surface of the plane F and another component of F is perpendicular to the plane F In theory this perpendicular component is equal to the normal force of the surface of the plane If there was no friction between the object and the plane the parallel component of the object s weight would accelerate the object down the plane However because there is friction between the object and the ...

Страница 48: ...ight 6 Calculate the perpendicular component F Mg cos of the block s weight and record this as the normal force FN 7 Use the normal force FN and the coefficient of sliding friction k for the surface material of the block either wood or felt to calculate the sliding friction force fk kFN 8 Calculate the weight of the hanging mass Fhanging mg and record this as the tension in the thread T 9 Calculat...

Страница 49: ...erpendicular component of the block s weight or F Mg cos The force of static friction fs is the coefficient of static friction s multiplied by the normal force Therefore fs s Mg cos When the block is at rest the static friction force equals the component of the block s weight that is parallel to the incline or Solving for the coefficient of static friction s gives the following Procedure 1 Mount t...

Страница 50: ...Statics System Static Friction on an Inclined Plane 46 012 12876B ...

Страница 51: ... the spring constant Whenever an object is acted on by a restoring force that is proportional to the displacement of the object from its equilibrium position the resulting motion is called Simple Harmonic Motion SHM When the simple harmonic motion of a mass M on a spring is analyzed mathematically using Newton s Second Law and calculus the period of the motion T is as follows The period T is the a...

Страница 52: ...for the 125 g mass five times Calculate and record the Average Measured Period 6 Use M and k to calculate the Theoretical Period Ttheoretical and record the result 7 Repeat the procedure using masses of 175 g and 225 g total mass including the mass hanger Data Table Questions 1 How well does the theoretical value for the period of oscillation compare to the measured period of oscilla tion 2 Does t...

Страница 53: ...erage Measured Period and k is the spring constant After calculating the total mass based on the average measured period and the spring constant recalculate the the oretical period based on the calculated total mass and the spring constant Compare the calculated total mass Mtotal to the hanging mass M Approximately how much extra mass is oscillating in addition to the hanging mass Mextra _________...

Страница 54: ...net torque causes angular acceleration that is directly proportional to the torque and inversely proportional to the rotational inertia I That is 0 or I Setting the two expressions for torque equal to each other gives FL I Assume that the beam is like a thin rod pivoted around one end The rotational inertia of the thin rod is I 1 3 m L2 where m is the mass of the beam Since the force on the beam i...

Страница 55: ...ct the Angle Indicator on the Protractor to the bottom hook of the Spring Scale 4 Adjust the Balance Arm and the Spring Scale so that the arm is horizontal and the scale is vertical and directly above the center of the protractor 5 Push the balance arm down and release it smoothly Measure the time for at least ten complete oscillations down up down Record the number of oscillations and the total t...

Страница 56: ... not Extension The rod and part of the spring in the Spring Scale oscillate up and down as the beam oscillates Use your results from the first part of this experiment to calculate the total mass that oscillates the arm and protractor plus the mass of the parts of the Spring Scale that also oscillate Recalculate the theoretical period Ttheoretical How does the re calculated theoretical period compa...

Страница 57: ...ial component of the weight mg sin is in the direction of motion and accelerates or decel erates the mass Using the congruent triangles in the figure it can be seen that the displacement of the mass from the equilibrium position is an arc whose length x is approximately L tan If the angle is relatively small less than 20 then it is very nearly true that sin tan Therefore for small swings of the pe...

Страница 58: ...l less than 20 Measure the time for 30 oscillations Record the total time 5 Repeat the measurement five times 6 Change the mass Repeat the procedure for a 20 g hanging mass and then a 50 g hang ing mass 7 Change the length Repeat the procedure for the original mass and two different pen dulum lengths one half of the original length and then one quarter of the original length Data Table Mass 1 kg L...

Страница 59: ...ompare to the mea sured period of oscillation 2 Does the equation for the period of a simple pendulum provide a good mathematical model for the physical reality Why or why not 3 How does increasing the mass of the simple pendulum affect the period of the pendulum 4 How does changing the length of the simple pendulum affect the period of the pendulum Mass 1 kg Length 2 m Oscillations Total Time s M...

Страница 60: ...Statics System Exp 10 Simple Harmonic Motion The Simple Pendulum 56 012 12876B ...

Страница 61: ...ia rotational inertia for the physical pendulum replaces M and Lcm mg replaces k in the equation for the period of oscillation of a mass on a spring Assume that the Balance Arm beam is a rectangular type rod For a rod pivoting around an axis through its center of mass the moment of inertia around the center of mass is where m is the mass and L is the length of the rod What happens if the rod pivot...

Страница 62: ... 0 3 Start the beam swinging but keep the angle of the swing reasonably small less than 20 4 Measure and record the total time for 10 oscillations 5 Repeat the measurement a total of five times Data Table Length L m _________________ Distance Lcm m _______________ Calculations 1 For each trial calculate and record the Measured Period by dividing the total time by the number of oscilla tions Calcul...

Страница 63: ...en the formula for Iparallel gives a simpler expression Substituting this expression into the formula for the period of oscillation of a physical pendulum gives Use this expression to re calculate the theoretical period of the physical pendulum and compare the result to the measured period of oscillation How much difference is there between the re calculated theoretical period and the previous the...

Страница 64: ...e outline of the pivot base onto the board 3 Hold the dry erase pen or pencil at the end of the beam and perpendicular to the board and move the beam and pen so you draw an arc from the bottom corner of the board to the opposite top corner 4 After you draw the arc remove the Balance Arm and place the base of the Force Wheel into the outline of the pivot base Level the Force Wheel Item Item Statics...

Страница 65: ...m so its center line points at the 5 mark on the arc Release the beam and measure the time for at least ten oscillations Record the time and the number of oscillations 2 Hold the beam so its center line points at the 10 mark and repeat the measurement 3 Continue to measure and record the total time for at least ten oscillations at each angle until you reach 90 Data Table Analysis 1 Calculate and r...

Страница 66: ...Statics System Exp 11A Simple Harmonic Motion Physical Pendulum 62 012 12876B ...

Страница 67: ...e m is the mass and L is the length of the rod If the rod pivots around any other axis that is parallel to the axis through the center of mass the Parallel Axis The orem states that the moment of inertia about the parallel axis Iparallel is the sum of the moment of inertia around the center of mass Icm plus mLcm 2 where m is the mass of the rod and Lcm is the perpendicular distance from the center...

Страница 68: ... for 10 oscillations 4 Change the position of the beam so that the pivot point is one centimeter farther from the center of mass Repeat the measurement for the total time of oscillation 5 Increase the distance Lcm by one centimeter again and repeat the procedure 6 Increase the distance Lcm by one centimeter until you reach the 170 mm mark on the beam 7 Record the total length L of the beam Total l...

Страница 69: ... and solve for Lcm to confirm that this distance is Calculate and record the value for Lcm based on the total length L Theoretical Lcm _______________ Questions 1 Based on the graph for which distance from the pivot point to the center of mass Lcm is the period a mini mum 2 How does the value from the graph for the distance that gives minimum period compare to the theoretical calculated value for ...

Страница 70: ...Statics System Exp 11B Minimum Period of a Physical Pendulum 66 012 12876B ...

Страница 71: ...ring is FLlever A net torque causes angular acceleration that is directly proportional to the torque and inversely proportional to the moment of inertia I That is or I Setting the two expressions for torque equal to each other gives FLlever I or kxLlever I where x is the displacement of the spring up and down as it oscillates The angular acceleration and the tangential linear acceleration aT of th...

Страница 72: ...mm mark Mount the Balance Arm beam on the Statics Board 3 Mount the Spring Scale on the Statics Board so that the scale is perfectly vertical Use thread to connect the Angle Indicator on the Protractor to the bottom hook of the Spring Scale 4 Adjust the Balance Arm and the Spring Scale so that the arm is horizontal and the scale is directly above the center of the protractor 5 Push the Balance Arm...

Страница 73: ...a point mass m at a distance r from the axis of rotation Its moment of inertia added to the beam s moment of inertia gives the following Since the distance r from the axis of rotation is also the length of the lever arm Llever the moment of inertia becomes and the period of oscillation T becomes 3 Calculate the Theoretical Period Ttheoretical for each trial and record the result Data mass of beam ...

Страница 74: ...oscillation for each trial 2 Does the equation for the period of a beam on a spring provide a good mathematical model for the actual period of a beam on a spring Why or why not Llever m Oscillations Total Time s Measured Period s Theoretical Period s 0 060 Average Measured Period s 0 070 Average Measured Period s 0 080 Average Measured Period s 0 090 Average Measured Period s 0 100 Average Measure...

Страница 75: ...imple Harmonic Motion Beam on a Spring 012 12876B 71 Extension Plot a graph of period T versus the reciprocal of Llever Determine the slope of the line and compare the slope s value to the following 2 1 12 ML 2 MLcm 2 mLlever 2 k ...

Страница 76: ...Statics System Exp 11C Simple Harmonic Motion Beam on a Spring 72 012 12876B ...

Страница 77: ...lacement of the object in the direction of the force If a force is applied to an object but the object does not move in the direction of the force then technically no work is done Whenever work is done on an isolated system the energy of the system will change by exactly the amount of work that was performed or E W where E is the change of energy In this experiment you will apply a measurable amou...

Страница 78: ... to outline the base of the Spring Scale and the position of the top of the Hanging Mass on the Statics Board 3 Slowly push the Spring Scale upward If you perform this movement slowly enough the reading on the Spring Scale will not vary appreciably 4 Mark the new positions of the Hanging Mass and the Spring Scale 5 Measure and record the distances d1 distance Hanging Mass moved and d2 distance Spr...

Страница 79: ...make it easier to perform work such as raising a heavy load Explain in terms of conserva tion of energy Extension The type of lever that has the fulcrum between the load hanging mass and the applied force Spring Scale is called a Class I Lever A Class II Lever has the load between the fulcrum and the applied force and the Class III lever has the applied force between the fulcrum and the load Item ...

Страница 80: ...ques equals the sum of the counterclockwise torques for the Class II and Class III levers Will you need to take the mass of the pro tractors and the mass of the Balance Arm beam into account Diagram your results and show your measurements and calculations on a separate sheet of paper Data Table Questions 1 For the Class II Lever is the net torque equal to zero when the lever is in equilibrium 2 Fo...

Страница 81: ... but the distance over which the force acts is longer The angle is the incline of the plane Procedure 1 Put a 100 g mass on the peg of the Mass Cart and use the Spring Scale to measure the total weight W of the cart plus mass Weight W ______________ 2 Put the Inclined Plane on the Statics Board at a relatively small angle such as 15 Put a Pulley and the Spring Scale on the board near one end of th...

Страница 82: ...alculations 1 Calculate and record the height that the Mass Cart was lifted as it was pulled up the Inclined Plane by the Spring Scale Height d1 sin ________________ 2 Calculate and record the amount of work done by the Spring Scale Work F1 d1 _________________ 3 Calculate and record the change in gravitational potential energy of the Mass Cart E Weight x height W d1 sin __________________ Questio...

Страница 83: ... Cart by lifting it straight up by a distance of d1 sin Work F d F2 d1 sin ___________________ 2 Calculate and record the change in gravitational potential energy of the Mass Cart E Weight x height W d1 sin __________________ Questions 1 How does the work done on the Mass Cart when it was on the Inclined Plane compare to the work done when it was lifted directly by the Spring Scale 2 How does an i...

Страница 84: ...Statics System Exp 13 Simple Machines The Inclined Plane 80 012 12876B ...

Страница 85: ...cts of friction in the pulleys 1 Put 200 g of mass on a mass hanger and use the Spring Scale to measure the total weight W of the mass hanger plus mass Record your measurement Weight W ______________ 2 Put the Spring Scale and two Pulleys on the Statics Board as shown and use thread to attach the Spring Scale to the hanging mass Record the reading of the force F on the Spring Scale Force F _______...

Страница 86: ... that the hanging mass was raised Data Table Questions 1 How does the relationship of weight W and force F compare to the relationship of the distance the Spring Scale was raised d1 and the distance the hanging mass was raised d2 2 Compare the value of W F to the number of threads that crosses the dotted line in the figure of the pulley sys tem System W F W F d1 d2 Work E A B C Figure 14 3 Pulley ...

Страница 87: ... in the cable Another torque is produced by the weight of the beam A third torque is produced by the weight of the hanging mass where W is the weight of the hanging mass L is the lever arm from the pivot point to the place where the hanging mass is attached Wboom is the weight of the boom Lcm is the lever arm from the pivot point to the center of mass is the angle of the boom T is the tension in t...

Страница 88: ...necessary measurements Data Table Calculations 1 Calculate the sum of the clockwise torques about the pivot point torqueclockwise _____________________ 2 Calculate the theoretical tension T in the thread Tensiontheoretical ________________________ Question How does the force reading on the Spring Scale compare to the theoretical value for the tension in the cable Item Value Angle of Balance Arm An...

Страница 89: ... complicates the demonstration In the free body diagram FBD of the Atwood s Machine T is the tension in the string Mass2 is greater than Mass1 and g is the acceleration due to gravity Using the convention that up is positive and down is negative the net force equations for the two masses are Ideally where the string is massless and doesn t stretch and the pulley is massless and frictionless the te...

Страница 90: ...nd the total mass for M2 in the Data Table 3 Move the 1 g mass from the light mass hanger to the heavy mass hanger so the difference in mass is 1 g Pull the light mass hanger down so that the bottom edge of the heavy mass hanger is aligned with the starting mark on the Statics Board NOTE Stop the hangers from spinning or swinging 4 Release the light mass hanger and start timing at the same instant...

Страница 91: ...the time t1 in the Data Table Repeat the trial two more times and record the results 5 For the second trial add 20 g of mass to each hanger but M still is 5 g Repeat the data recording procedure three times 6 For the third trial add another 20 g of mass to each hanger and repeat the procedure three times 7 For the fourth trial add another 20 g of mass to each hanger and repeat the procedure three ...

Страница 92: ...graph of net force vertical axis versus measured acceleration horizontal axis Questions 1 Describe the graph of net force versus measured acceleration What does the slope of this graph represent 2 How does the plot of net force versus measured acceleration relate to Newton s Second Law 3 Compare the percent difference for the theoretical and measured accelerations What are some reasons that might ...

Страница 93: ...any part of this manual providing the reproductions are used only in their laboratories and classrooms and are not sold for profit Reproduction under any other circumstances without the written con sent of PASCO scientific is prohibited Trademarks PASCO and PASCO scientific are trademarks or registered trademarks of PASCO scientific in the United States and or in other countries All other brands p...

Страница 94: ...Statics System Technical Support 90 012 12876B ...

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