A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion


 Junior Lee
 4 years ago
 Views:
Transcription
1 A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for different known masses m 1 and m 2. You will then use these results to obtain g, the acceleration due to gravity. You will also learn how to deal with random errors and systematic errors in experiments. Equipment Cart, pulley with mounting clamps, string, spark timer, timing tape, wood stop, table clamp, weight hanger, weights, sand bag, masking tape, ruler and triple beam balance. Introduction In beginning physics, students test their ability to understand and apply Newton's second law by doing homework problems involving the constant acceleration of masses subject to constant net forces. The masses may be moving vertically or on surfaces that are horizontal or inclined, with or without friction. Often there are two or more masses involved connected by ropes with possibly one or more of the masses hanging from pulleys. Generally the mass of each object is given but the gravity force of the earth on it, i.e., its weight is not. To obtain the weight it is necessary to use the relation where g is called the acceleration due to gravity and must be given. Usually, the student is told that, although g varies with location, a good average value of g is 9.80 m/s 2 for motion near the earth's surface. In this experiment you will use an arrangement of the type described above to actually determine g at your laboratory location given some known masses, an understanding of Newton's second law and a record of the motion. Mass m 2 is a cart, able to roll (with some friction) on your lab table. m 2 is connected to the hanging mass m 1 by a light (negligible mass) string passing over a pulley. When the system is released from rest with the spark timer activated, the position of m 2 (and m 1 ) is recorded
2 as dots on the tape every 1/60 th of a second. It is clear that the acceleration of m 2 (and m 1 ) and the resulting record will depend on the value of g. (If you could do this experiment on the moon for instance, would you expect the acceleration of m 2 to be greater or less than that on earth? Why?) Theory Let T be the tension in the string while m 1 is moving downward. Then the string exerts an upward force T on m 1 and a force T to the right on m 2. Let f be the kinetic friction force opposing the motion of m 2. is the weight of m 1. These individual forces are shown in Figure 2a.2 below. (Note that the vertical forces on m 2 have been omitted as they will not be needed in this particular analysis.) The net force on m 1 is downward and equals m 1 g  T. The net force on m 2 is to the right and equals T  f. Since the accelerations of m 1 and m 2 must have the same magnitude, we can designate this magnitude by the letter a. Newton's second law when applied to m l and m 2 then gives: for m 1 and for m 2. On adding these two equations, the result is:. On solving for g, (2a.1)
3 Brief Comments on the Treatment of Experimental Errors Experimental error or uncertainty is inherent in any experimental result at some level, however small. It is set by a combination of the design of the experiment, the quality of the apparatus and the skill of the experimenter. Generally it is possible to separate the sources of experimental errors into two categories: random and systematic. A. Random Errors The existence of random errors in a measurement can be inferred if repetition of the measurement does not give the same result each time. By definition, random errors are those that tend to average out upon repetitions of the measurement. For random errors then, the more repetitions of a measurement the less the uncertainty in the resulting average. From the mathematics of statistics it can be shown that the uncertainty due to random error in the average of N measurements decreases as when N is "large". Thus 400 measurements should give an average with half the uncertainty due to random error as compared to 100 measurements. The first step in treating the random error in a large number N of repeated measurements is to calculate the average. The average is the desired result and it is the uncertainty of the average due to random errors which must then be determined. If the N measurements are labeled y 1, y 2, y 3,... y N the average as denoted by defined as: is (The average is also sometimes called the mean in statistics.) To establish the uncertainty in the average, the usual procedure is to first calculate what is called σ (sigma), the standard deviation of measurements. If it is believed that no one measurement is more accurate that any of the others (as we will assume) then σ is defined by: The significance of σ is that any one additional y measurement has about a 2 in 3 chance of falling between ± σ of the average,. Statistical analysis further shows that the average, has about a 2 in 3 chance of falling within ± σ of the true value. Thus, after specifying the average of N repeated measurements, it is common to append ± σ as a measure of the uncertainty due to the randomness of the measurements.
4 Example Suppose you have the following 5 measurements of the same quantity. Note: One or two more decimal points must be kept in the calculations than are in the data until the calculations are complete. The standard deviation of these measurements is: The uncertainty in the average is = The result is then ± At this point some rounding off is appropriate and the result would be reported as 1.04 ± 0.01 or possibly as ± It should be pointed out that the number 5 is stretching the concept of large N beyond reasonable bounds but that this is common practice when a large number of measurements are not available. B. Systematic Errors A systematic error is one which tends to repeat and thus create a shift in the average from the true value. Systematic errors may be provided by the experimenter, the apparatus or by poor design of the experiment. Because they are not revealed by repeated measurements, care must be exercised to investigate and account for all possible sources of systematic errors. This can be very difficult to do. Such errors sometimes remain unknown until other experimenters with other apparatus obtain convincing evidence that a previous result is off by more than the originally reported uncertainty.
5 Error Analysis in 2048C Laboratory Experiments A. Treatment of Random Errors Generally in your lab experiments in 2048C you will not measure the same quantity over and over. Often, however, you will have a moderate number of data points which are used to determine a single experimental quantity. Under such circumstances the data can be treated in two ways. The first way is the graphical method such as you used in the g experiment where the data are used to create a straight line plot the slope of which is the desired experimental quantity. The second way is to convert the data to a form equivalent to a series of repeated measurements. In the case of the g experiment, this would correspond to determining the accelerator between every pair of data points on the tape and creating a whole set of values for acceleration a, which you would then average. In general the graphical method is preferable and it is the only one you will use. It has the advantage that it gives a useful visual picture of the data. It allows you to see whether, in fact, the data exhibit the expected linear behavior and it also makes it easy to see the scatter or random errors in the data. To treat the random errors in your data using the second (nongraphical) approach you would use the results presented earlier for repeated measurements to calculate the uncertainty in the average. In the case of the graphical approach, the random errors in the data points produce a statistical error or uncertainty in the slope. The statistical treatment of random data errors in the graphical approach involves the same principles, but somewhat different mathematics, as the treatment for the effect of random errors in repeated measurements. These mathematics will not be discussed in this course in any detail but have been embodied in a computer program which you will use inside Excel. This program will analyze and plot your data and give you the uncertainty in the slope produced by random errors in your data. B. Treatment of Systematic Errors You will be expected to discuss for each experiment possible sources of systematic errors. In general, this means giving plausible reasons as to why your results might differ from the expected result by more than the uncertainty due to random error. Procedure Set up the equipment as shown in Figure 2a.1. Set the length of the string so that the hanging mass m 1 will not hit the floor when the cart reaches the edge of the table. Use about 30 cm of timer tape and adjust for at least 40 cm travel of m l and the cart. Fasten the tape to the bottom of the cart with a masking tape.
6 The amount of data which you will take in this experiment and the time required to obtain it are both small. Whether you obtain good data or not hinges on your experimental skills and attention to instructions. You must observe the following precautions while setting up. 1. Be sure that the pulley height is adjusted so that the string from the pulley to the cart is horizontal. 2. Be sure that the pulley, the cart, and the timer are all in one line with the cart aimed at the pulley. To take data, hold the cart in a steady position with m 1, just below the pulley. Have your partner take any slack out of the timing tape and then have him or her start the timer. Wait an instant for the timer to come up to speed and then abruptly release the cart. Practice the above once or twice before taking any data. Take at least three motion records with the following values of m 1 and m 2 : 1) m 1 = kg, m 2 = cart 2) m l = kg, m 2 = cart 3) m 1 = kg, m 2 = cart plus sandbag. As you obtain each tape, write on it the values for m l and m 2 so you do not get the tapes mixed up later. Inspect your tapes to see if the timer marks appear consistent with motion that starts from rest and increases in speed as time goes on. When you are convinced that you have reasonable looking tapes, ask your instructor to look at them to see if he or she concurs. Determine the force of friction using the following method: Since friction is not negligible in this experiment, the kinetic friction force, f, opposing the motion must be measured. To do this we use Newton's first law. That is, if you hang a weight on the string that produces a force equal and opposite to the kinetic friction, then the cart once set into motion ought to move at constant velocity. With m 2 = cart, start by using a mass m = 25 g initially. Give the cart a nudge and observe the motion. Increase or decrease m as needed to produce a constant velocity. You can determine the needed value of m to produce a constant velocity by direct observation. Be sure to determine the friction force for all values of m 2 that you use. Because the friction force is now given by mg and you are to determine g in this experiment, you must replace f by mg in Equation (2a.1) and solve for g. Show that the result is:
7 (2a.2) Data Analysis The assumption in this experiment (which your graphs should verify) is that the friction force is constant. If so, it follows from Equation 2a.1 or 2a.2 that the acceleration a is constant. In this case the distance, D, that the cart travels in time, t, is given by: (2a.3), and the instantaneous velocity, v, of the cart after time, t, is: (2a.4), Since the cart is released from rest, it is true that v o = 0 at the instant of release. However, your timer may not have made a mark at just that instant or you may not have released the cart cleanly. In any case, the likely uncertainty as to which tape mark represents t = 0 makes Equation 2a.4 rather than 2a.3 the best choice for analyzing the data. You should recognize that Equation 2a.4, is of the form so that a graph of v versus t on linear paper should be a straight line whose slope is the acceleration a. Figure 2a.3 illustrates this. Note that if you were to change the instant of time that you label t = 0, the graph would be shifted horizontally. v o, the intercept on the v axis, would change but the slope representing
8 the acceleration a would remain the same. Hence, such a graph will give a value for a unaffected by any initial timing uncertainty. Since the marks on the tape represent distances traveled, you will have to use these distances to determine instantaneous velocities in order to plot Equation 2a.4. To do this, measure and record the distances ΔD in cm between the centers of successive timing marks. Pick a convenient point to start measuring and try to measure as many distances as you can. Carefully measure to at least the nearest 0.05 cm (half a millimeter). Use your clear plastic ruler to do this. Omit measuring values of ΔD that are less than 3 or 4 millimeters. Also do not include the last two or three points on the tape as they may have been recorded when the cart was stopped by the wood block. Run Excel and enter in separate columns the measured distances ΔD and the corresponding time t in seconds for each of your tapes. Identify each run and record the corresponding cart mass m 2, mass of the pulling weight m 1, and the mass of the hanging weight m used to determine friction force. As discussed, the time you choose to call t = 0 doesn't matter in determining the acceleration from the graph of Equation 2a.4. It is convenient to let t = 1/60 s = s correspond to your first value of t. m 1 = m 2 = m = Time in seconds Measured ΔD in cm v = ΔD/Δt in cm/s In another column, calculate the velocity v (by using equations in Excel, do not use your calculator to do this) for each time interval by dividing ΔD by 1/60 sec which is the length of each time interval corresponding to ΔD. Graph v versus t using the Regression feature of Excel which can be obtained from Tools Data Analysis menu. The time t should be plotted on the xaxis and the measured distances ΔD on the yaxis. Make sure to click on
9 the boxes for Residuals, Residual Plots, Line Fit Plots and New Worksheet Ply to produce the information and graphs that you need for analysis. Go to your Line Fit Plot. Add a trend line and display the equation of the best fit line for v versus t. Get the slope of this line (what does this slope represent?). Also determine the uncertainty in the slope by inspecting the resulting tables. Repeat the calculation of velocity v and the graphing instructions on this paragraph for the other 2 runs. Because of the linear relation between v and t in Equation 2a.4, the average velocities you have determined are also instantaneous velocities midway through the time interval between marks. Hence a plot of your versus t on linear graph paper will give you a plot whose slope is the acceleration a. Calculate the value for the acceleration due to gravity g for each of your runs using Equation 2a.2 and your values for a, m 1, m 2 and m. Tabulate the 3 values of a and their uncertainties, and also the 3 values of g that you got. Calculate the standard deviation σ of the three measurements of g as a measure of its uncertainty due to the randomness of the measurements. Calculate the percentage difference between each of your results and the value of g = 980 cm/s 2 (9.80 m/s 2 ) expected at this location. NOTE: Include printouts of your data tables and graphs from Excel in your report. Also include the tabulation of the 3 values of a and the corresponding uncertainties, and also the 3 values of g, σ and the calculated percentage differences.
10 Questions: a. Inspect the Line Fit Plot and check how well the measured values of the velocity v plotted on the y axis coincide with the Predicted Y on the computer fitted line. Inspect the Residuals and the Residual Plot. Are your residuals reasonable or are there obvious outliers or data points that are possibly entered in error? b. By how much do each of your values for g differ from 980 cm/s 2? How does each difference compare with the corresponding uncertainty Δg due to the random errors in the data? Does it appear that there is a systematic error in either or both of your results? c. If you worked carefully and your equipment worked properly, you may see the effect of a small systematic error inherent in the design of this experiment. In order to get the cart wheels to spin faster and faster as the cart accelerates, the table must exert a static friction force on the wheel rim in a direction opposite to the cart motion. This is not the friction force you measured when the cart was moving at constant velocity and so it has not been accounted for. A calculation of this retarding force on the cart based on the mass and geometry of the wheels and the physics of circular motion shows that it should cause the measured value of g to come out about 2% low for the values of m 1, and m 2 used here. What result do you obtain if your g values are each increased by 2% (about 20 cm/s 2 ) to account for the systematic errors above? Are your data accurate enough to see this effect? Do you still have systematic errors larger than the above? d. List a few other possible sources of systematic errors that should be checked if time allowed. (Hint: Think about some of the assumptions you likely have made about the equipment that may or may not be valid.) Because each run was made under different conditions, i.e., with different masses, they do not represent an exact repetition of a single measurement. Each run may be subject therefore, to different systematic errors. Until such errors are accounted for, averaging of your results is not strictly valid Dr. H. K. Ng. All Rights Reserved. Revised Fall 2013 B. R. Reyes
LAB 6: GRAVITATIONAL AND PASSIVE FORCES
55 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 by the attraction
More informationLAB 6  GRAVITATIONAL AND PASSIVE FORCES
L061 Name Date Partners LAB 6  GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies
More informationNewton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of
Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed
More informationGeneral Physics Lab: Atwood s Machine
General Physics Lab: Atwood s Machine Introduction One may study Newton s second law using a device known as Atwood s machine, shown below. It consists of a pulley and two hanging masses. The difference
More informationConservation of Energy Physics Lab VI
Conservation of Energy Physics Lab VI Objective This lab experiment explores the principle of energy conservation. You will analyze the final speed of an air track glider pulled along an air track by a
More informationEXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives
EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives to verify how the distance of a freelyfalling body varies with time to investigate whether the velocity
More informationExperiment: Static and Kinetic Friction
PHY 201: General Physics I Lab page 1 of 6 OBJECTIVES Experiment: Static and Kinetic Friction Use a Force Sensor to measure the force of static friction. Determine the relationship between force of static
More informationPrelab Exercises: Hooke's Law and the Behavior of Springs
59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically
More informationACCELERATION DUE TO GRAVITY
EXPERIMENT 1 PHYSICS 107 ACCELERATION DUE TO GRAVITY Skills you will learn or practice: Calculate velocity and acceleration from experimental measurements of x vs t (spark positions) Find average velocities
More informationKinetic Friction. Experiment #13
Kinetic Friction Experiment #13 Joe Solution E01234567 Partner Jane Answers PHY 221 Lab Instructor Nathaniel Franklin Wednesday, 11 AM1 PM Lecture Instructor Dr. Jacobs Abstract The purpose of this
More informationDetermining the Acceleration Due to Gravity
Chabot College Physics Lab Scott Hildreth Determining the Acceleration Due to Gravity Introduction In this experiment, you ll determine the acceleration due to earth s gravitational force with three different
More informationTwoBody System: Two Hanging Masses
Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.
More informationSTATIC AND KINETIC FRICTION
STATIC AND KINETIC FRICTION LAB MECH 3.COMP From Physics with Computers, Vernier Software & Technology, 2000. INTRODUCTION If you try to slide a heavy box resting on the floor, you may find it difficult
More informationKinetic Friction. Experiment #13
Kinetic Friction Experiment #13 Joe Solution E00123456 Partner  Jane Answers PHY 221 Lab Instructor Chuck Borener Thursday, 11 AM 1 PM Lecture Instructor Dr. Jacobs Abstract In this experiment, we test
More informationLaboratory Report Scoring and Cover Sheet
Laboratory Report Scoring and Cover Sheet Title of Lab _Newton s Laws Course and Lab Section Number: PHY 1103100 Date _23 Sept 2014 Principle Investigator _Thomas Edison CoInvestigator _Nikola Tesla
More informationPHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17. February 13, 2013
PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17 February 13, 2013 0.1 A 2.00kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationDetermination of g using a spring
INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationWork and Energy. W =!KE = KE f
Activity 19 PS2826 Work and Energy Mechanics: workenergy theorem, conservation of energy GLX setup file: work energy Qty Equipment and Materials Part Number 1 PASPORT Xplorer GLX PS2002 1 PASPORT Motion
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More informationRotational Motion: Moment of Inertia
Experiment 8 Rotational Motion: Moment of Inertia 8.1 Objectives Familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body
More informationCoefficient of Friction Using a Force Sensor and a Motion Sensor
Physics Laboratory Manual n Loyd LABORATORY 7A Coefficient of Friction Using a Force Sensor and a Motion Sensor OBJECTIVES o Investigate the coefficient of static friction between a feltcovered wood block
More informationLab 8: Ballistic Pendulum
Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationTorque and Rotary Motion
Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straightforward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,
More informationAP Physics  Chapter 8 Practice Test
AP Physics  Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on
More informationConceptual Questions: Forces and Newton s Laws
Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationAP Physics C Fall Final Web Review
Name: Class: _ Date: _ AP Physics C Fall Final Web Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. On a position versus time graph, the slope of
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationOne and Twodimensional Motion
PHYS101 LAB02 One and Twodimensional Motion 1. Objective The objectives of this experiment are: to measure the acceleration of gravity using onedimensional motion to demonstrate the independence of
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationCOEFFICIENT OF KINETIC FRICTION
COEFFICIENT OF KINETIC FRICTION LAB MECH 5.COMP From Physics with Computers, Vernier Software & Technology, 2000. INTRODUCTION If you try to slide a heavy box resting on the floor, you may find it difficult
More informationPhysics Lab Report Guidelines
Physics Lab Report Guidelines Summary The following is an outline of the requirements for a physics lab report. A. Experimental Description 1. Provide a statement of the physical theory or principle observed
More information5. Forces and MotionI. Force is an interaction that causes the acceleration of a body. A vector quantity.
5. Forces and MotionI 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will
More informationAcceleration of Gravity Lab Basic Version
Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration
More information1 of 7 9/5/2009 6:12 PM
1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationSerway_ISM_V1 1 Chapter 4
Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As
More informationChapter 4: Newton s Laws: Explaining Motion
Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state
More informationExperiment 5 ~ Friction
Purpose: Experiment 5 ~ Friction In this lab, you will make some basic measurements of friction. First you will measure the coefficients of static friction between several combinations of surfaces using
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationOscillations: Mass on a Spring and Pendulums
Chapter 3 Oscillations: Mass on a Spring and Pendulums 3.1 Purpose 3.2 Introduction Galileo is said to have been sitting in church watching the large chandelier swinging to and fro when he decided that
More informationIf you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ
Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces
More informationChapter 11 Equilibrium
11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of
More informationFREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5
Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities
More informationAcceleration due to Gravity
Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision
More informationNewton s Law of Motion
chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationWhen showing forces on diagrams, it is important to show the directions in which they act as well as their magnitudes.
When showing forces on diagrams, it is important to show the directions in which they act as well as their magnitudes. mass M, the force of attraction exerted by the Earth on an object, acts downwards.
More information5.1 The First Law: The Law of Inertia
The First Law: The Law of Inertia Investigation 5.1 5.1 The First Law: The Law of Inertia How does changing an object s inertia affect its motion? Newton s first law states that objects tend to keep doing
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationGENERAL SCIENCE LABORATORY 1110L Lab Experiment 5 THE SPRING CONSTANT
GENERAL SCIENCE LABORATORY 1110L Lab Experiment 5 THE SPRING CONSTANT Objective: To determine the spring constant of a spiral spring Apparatus: Pendulum clamp, aluminum pole, large clamp, assorted masses,
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME9472), string with loop at one end and small white bead at the other end (125
More informationPendulum Force and Centripetal Acceleration
Pendulum Force and Centripetal Acceleration 1 Objectives 1. To calibrate and use a force probe and motion detector. 2. To understand centripetal acceleration. 3. To solve force problems involving centripetal
More information6. Block and Tackle* Block and tackle
6. Block and Tackle* A block and tackle is a combination of pulleys and ropes often used for lifting. Pulleys grouped together in a single frame make up what is called a pulley block. The tackle refers
More informationExperiment 9. The Pendulum
Experiment 9 The Pendulum 9.1 Objectives Investigate the functional dependence of the period (τ) 1 of a pendulum on its length (L), the mass of its bob (m), and the starting angle (θ 0 ). Use a pendulum
More informationPart 1: Background  Graphing
Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background  Graphing In science it is very important to find and
More informationAt the skate park on the ramp
At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises
More informationACTIVITY 6: Falling Objects
UNIT FM Developing Ideas ACTIVITY 6: Falling Objects Purpose and Key Question You developed your ideas about how the motion of an object is related to the forces acting on it using objects that move horizontally.
More information4 Gravity: A Force of Attraction
CHAPTER 1 SECTION Matter in Motion 4 Gravity: A Force of Attraction BEFORE YOU READ After you read this section, you should be able to answer these questions: What is gravity? How are weight and mass different?
More informationThe Force Table Vector Addition and Resolution
Name School Date The Force Table Vector Addition and Resolution Vectors? I don't have any vectors, I'm just a kid. From Flight of the Navigator Explore the Apparatus/Theory We ll use the Force Table Apparatus
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problemsolving questions, draw appropriate free body diagrams and use the aforementioned problemsolving method.. Define the following
More informationAP Physics 1 and 2 Lab Investigations
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
More informationCurso20122013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationENERGYand WORK (PART I and II) 9MAC
ENERGYand WORK (PART I and II) 9MAC Purpose: To understand work, potential energy, & kinetic energy. To understand conservation of energy and how energy is converted from one form to the other. Apparatus:
More informationConservation of Momentum and Energy
Conservation of Momentum and Energy OBJECTIVES to investigate simple elastic and inelastic collisions in one dimension to study the conservation of momentum and energy phenomena EQUIPMENT horizontal dynamics
More informationSimple Harmonic Motion
Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationThree Methods for Calculating the Buoyant Force Gleue: Physics
Three Methods for Calculating the Buoyant Force Gleue: Physics Name Hr. The Buoyant Force (F b ) is the apparent loss of weight for an object submerged in a fluid. For example if you have an object immersed
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationE X P E R I M E N T 8
E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:
More informationLesson 3  Understanding Energy (with a Pendulum)
Lesson 3  Understanding Energy (with a Pendulum) Introduction This lesson is meant to introduce energy and conservation of energy and is a continuation of the fundamentals of roller coaster engineering.
More informationAP Physics Applying Forces
AP Physics Applying Forces This section of your text will be very tedious, very tedious indeed. (The Physics Kahuna is just as sorry as he can be.) It s mostly just a bunch of complicated problems and
More informationGENERAL SCIENCE LABORATORY 1110L Lab Experiment 3: PROJECTILE MOTION
GENERAL SCIENCE LABORATORY 1110L Lab Experiment 3: PROJECTILE MOTION Objective: To understand the motion of a projectile in the earth s gravitational field and measure the muzzle velocity of the projectile
More information8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight
1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled
More informationUsing Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data
Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable
More informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More informationGraphing Motion. Every Picture Tells A Story
Graphing Motion Every Picture Tells A Story Read and interpret motion graphs Construct and draw motion graphs Determine speed, velocity and accleration from motion graphs If you make a graph by hand it
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationExperiment 4. Vector Addition: The Force Table
ETSU Physics and Astronomy Technical Physics Lab Exp 4 Page 29 Experiment 4. Vector Addition: The Force Table As we have learned in lecture, to the extent that pulleys are massless and frictionless, they
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationWork Energy & Power. September 2000 Number 05. 1. Work If a force acts on a body and causes it to move, then the force is doing work.
PhysicsFactsheet September 2000 Number 05 Work Energy & Power 1. Work If a force acts on a body and causes it to move, then the force is doing work. W = Fs W = work done (J) F = force applied (N) s = distance
More informationTEACHER ANSWER KEY November 12, 2003. Phys  Vectors 11132003
Phys  Vectors 11132003 TEACHER ANSWER KEY November 12, 2003 5 1. A 1.5kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude
More information0 Introduction to Data Analysis Using an Excel Spreadsheet
Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationTIphysics.com. Physics. Bell Ringer: Mechanical Advantage of a Single Fixed Pulley ID: 13507
Bell Ringer: Mechanical Advantage of a Single Fixed Pulley ID: 13507 Based on an activity by Irina Lyublinskaya Time required 15 minutes Topic: Work and Energy Calculate the mechanical advantages and efficiencies
More informationExperiment #9, Magnetic Forces Using the Current Balance
Physics 182  Fall 2014  Experiment #9 1 Experiment #9, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify
More informationACCELERATION DUE TO GRAVITY
ACCELERATION DUE TO GRAVITY Objective: To measure the acceleration of a freely falling body due to gravitational attraction. Apparatus: Computer with Logger Pro, green Vernier interface box, picket fence
More informationELASTIC FORCES and HOOKE S LAW
PHYS101 LAB03 ELASTIC FORCES and HOOKE S LAW 1. Objective The objective of this lab is to show that the response of a spring when an external agent changes its equilibrium length by x can be described
More informationChapter 6 Work and Energy
Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationIDEAL AND NONIDEAL GASES
2/2016 ideal gas 1/8 IDEAL AND NONIDEAL GASES PURPOSE: To measure how the pressure of a lowdensity gas varies with temperature, to determine the absolute zero of temperature by making a linear fit to
More informationANSWER KEY. Work and Machines
Chapter Project Worksheet 1 1. inclined plane, wedge, screw, lever, wheel and axle, pulley 2. pulley 3. lever 4. inclined plane 5. Answers will vary: top, side, or bottom 6. Answers will vary; only one
More information