...MEASUREMENT OF THE SPRING CONSTANT TWO METHODS COMPARED ABSTRACT A spring is an elastic object, which can be extended and contracted by forces with a constant elastic coefficient. This report assesses two methods for determining the spring constant of a specific spring. One method uses the length that the spring extends and the masses that are attached to the spring. The other method measuring the spring constant is based on the harmonic motion. INTRODUCTION Spring constant is an instinct property of a spring. The magnitude of a spring constant depends on the material of the spring but not the lengths it extends or contracts or the forces that are applied to the spring. Hook’s law predicts that the length the spring extends or contracts is directly proportional to the force applied by the coefficient of the spring constant. The aim of this experiment is to compare the two measures of finding the value of the spring constant of a spring. MATERIALS AND METHODS METHOD A The spring is hanged on an iron stand. The lengths of the spring, L, are measured when the spring is attached to different masses, M, of metals vertically. The lengths are measured by using a ruler with scales, while the mass attached to the spring can be read from the metal. For better accuracy, five masses are attached during this method. METHOD B The spring is hanged on an iron stand. Different masses, m, attached to the spring can be read from the metals and the time period, t, of the spring finishing...
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...Title: How different springs behave under the influence of same mass depending on the spring constant (k) and connection types (parallel or series)? Summary: This experiment will be carried out to investigate spring constants of different springs by measuring the length of springs under the influence of same mass and different masses, and observe how overall spring constant changes depending on connection types of springs by measuring amount of extension when springs are connected in series and parallel. Different springs with different constant, different masses, weighing machine and a measuring ruler will be used. Research: The course textbook and different textbooks (S.Beichner, Fizik1, Ankara: Palme Yayınevi, 2002.), some laboratory experiments, which retrieved from the Internet, some lectures and videos comprise sources for the theoretical analysis of the experiment. -Prof. Walter Lewin (1999), Hooke's Law, Simple Harmonic Oscillator (online) (http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-10), -Combination of springs (online) (http://engineeronadisk.com/V2/book_modelling/engineeronadisk-10.html) -Sal Khan (2008), Intro to springs and Hooke's Law (online) (http://www.youtube.com/watch?v=ZzwuHS9ldbY) -Forces and elasticity (online) (http://www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/forces/forceselasticityrev2.shtml) -Deformation of materials (online) (http://qatemplates.everythingscience.co.z...
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...laboratory in Physics I, student explored the motions of a mass on a spring. More specifically students looked at oscillations (periods) with various masses. Students set a spring into vertical oscillations with suspended masses and measured the period of oscillation. Using this method, students found a spring constant of 30.30N/m. Results should have verified that the period of oscillation depended on the effective mass of the spring and the period of oscillation. Students recorded basic information such as the position of the mass before the spring is charged, the path of the mass, the peak of the oscillation, as well as the force the mass and the spring exert on each other. Data studio and a force sensor, and a position sensor was used to get accurate measurements of these values. Goal The purpose of this laboratory is to characterize the oscillation of a simple spring-mass system. Theory If a spring is stretched or compressed a small distance from its equilibrium position, the spring will exert a force on the body given by Hooke's Law, where is known as the spring force. The constant, , known as the spring constant, and is the displacement from the equilibrium position. The spring constant is a clue of the spring's strength. A large value for indicates that the spring is strong or stiff. A low value for means the spring is weak or flexible. Springs with large values can balance larger forces than springs with low values. The negative sign in indicates that the...
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...| |Fall 2010 Course Number: 14319 Instructor: Larry Caretto | Unit Two Homework Solutions, September 9, 2010 1 A frictionless piston-cylinder device initially contains 200 L of saturated liquid refrigerant-134a. The piston is free to move, and its mass is such that it maintains a pressure of 900 kPa on the refrigerant. The refrigerant is now heated until its temperature rises to 70oC. Calculate the work done during this process. The freely-moving piston can be interpreted as giving a constant pressure process such that P1 = P2 = P = 900 kPa. For a constant pressure process, the concept that the work is the area under the path is particularly simple. That area is a rectangle whose area is P (V2 – V1). We know that P is 900 kPa, and the initial volume is 200 L = 0.2 m3, but we have to find the final volume. Because this is a constant pressure process, the final pressure equals the initial pressure of 900 kPa (0.9 MPa) and we are given that the final state has a temperature of 70oC. From the superheat tables for refrigerant-134a in Table A-13 on page 930, we find that the specific volume at this temperature and pressure is 0.027413 m3/kg. In order to find the volume (V in m3 as opposed to the specific volume, v, from the property tables in m3/kg), we have to know the mass. We can find the mass from the initial volume and the value of the specific volume at the initial state of saturated liquid...
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...Unit Two Homework Solutions, September 9, 2010 1 A frictionless piston-cylinder device initially contains 200 L of saturated liquid refrigerant-134a. The piston is free to move, and its mass is such that it maintains a pressure of 900 kPa on the refrigerant. The refrigerant is now heated until its temperature rises to 70oC. Calculate the work done during this process. The freely-moving piston can be interpreted as giving a constant pressure process such that P1 = P2 = P = 900 kPa. For a constant pressure process, the concept that the work is the area under the path is particularly simple. That area is a rectangle whose area is P (V2 – V1). We know that P is 900 kPa, and the initial volume is 200 L = 0.2 m3, but we have to find the final volume. Because this is a constant pressure process, the final pressure equals the initial pressure of 900 kPa (0.9 MPa) and we are given that the final state has a temperature of 70oC. From the superheat tables for refrigerant-134a in Table A-13 on page 930, we find that the specific volume at this temperature and pressure is 0.027413 m3/kg. In order to find the volume (V in m3 as opposed to the specific volume, v, from the property tables in m3/kg), we have to know the mass. We can find the mass from the initial volume and the value of the specific volume at the initial state of saturated liquid at 900 kPa. At this pressure, we use the saturation table, A-12, on page 928, to find the specific volume of the saturated liquid, vf =...
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...Simple Harmonic Motion Aston University Engineering and Applied Science – Physics Lab Report 01/11/2014 Determination by simple harmonic motion of the acceleration due to gravity Introduction: A system undertaking simple harmonic motion (SHM) can be restrained very accurately. The period of the SHM depends both on the mass of the system and the strength of the force tending to restore the system to its equilibrium state). Oscillations are a common part of life, for instance the vibrations of a musical instrument which helps make sounds or the foundations of a car suspension which are assisted by oscillations. The main aims of this experiment was to determine if the oscillation of a mass which hung vertically from a spring; this oscillating system was used to measure the acceleration of earth due to gravity and to determine the accuracy of experimental results precisely. (http://www.pgccphy.net/1020/phy1020.pdf Theory: | | | Acceleration due to gravity The value of 9.8m/s/s acceleration is given to a free falling object, directing downwards towards Earth. Any object moving solely under the influence of gravity is known as acceleration of gravity and this vital quantity is denoted by Physicians as the symbol g. (http://www.physicsclassroom.com/class/1DKin/Lesson-5/Acceleration-of-Gravity) Simple harmonic motion This is everyplace where the acceleration is proportional and opposite to displacement to the continuous amplitude from the position...
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...Newton’s laws as well as to learn some interesting ideas about various types of motion along a single direction. We gain some valuable insights and tools so that when we generalize to study the motion of objects in the real three-dimensional world we are well prepared for that undertaking. The case studies in this chapter include motion when the net force is constant (we study the local gravitational force near the Earth), one-dimensional motion of an object in a fluid (where we show that there are frictional forces that vary with time), and the oscillatory motion of an object attached to a spring. After learning something about springs, we next consider the deformation of an elastic solid and the phenomenon of viscoelasticity. This is a topic of special interest in the study of structural biomolecules such as bone and blood vessels. We conclude the chapter with a discussion of the structure and dynamics of macromolecules, specifically illustrating how to apply Newton’s second law to the difficult problem of determining the molecular motions (here in one dimension) of the constituent atoms of a protein. 1. THE CONSTANT FORCE Very frequently in dealing with mechanics problems, we know the forces acting on an...
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...pulley system using the Atwood’s machine and using springs (2) in series and parallel to determine their spring constants and extensions when a mass is hanged from them. Newron’s second law states that the force on an object is directly proportional to the rate of change of momentum, which later gives the formula F =ma , m= mass and a is acceleration. Newton;s third law suggests that every action occurring on an object has an equal and opposite reaction when they occur in pairs, are acting in opposite directions and has same magnitude. In part one, we measure the acceleration of the mass pulley system using the photo gate. Data M1 = 151.25 g M2 =171.25 g Mean acceleration = 0.5992 m/s^2 Standard deviation 0.05463 Data Analysis Part 1 (Atwood’s Machine) – Formula and calculation of theoretical acceleration (ath) – A =(m1-m2)/(m1+m2) * g , ath= (0.17125-0.15125)/( 0.17125+0.15125)* 9.79 = 0.6083 m/s^2 % error = 0.05463/0.5592 *100 =9.76 % Formula and calculation of percent difference between ae and ath – % difference = (difference / A_th) *100 = (0.55992-0.6083) /0.6083 *100 =8.01% Part 2 (Springs in Series) – Hooke’s law equation – F = -Kx Calculation of spring constants, k1 and k2 using Hooke’s law equation – k1 = mg/ x = (2.75)/0.052 =52.9 k2 = mg/ x = (7.73)/ 0.058 = 90.9 Calculation of experimental keff for series combinations of springs – K eff = Fs / del(xs ) K = F/x =10.31...
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...given ten identical springs. Describe how you would develop a scale of force (ie., a means of producing repeatable forces of a variety of sizes) using these springs. Decide on an extension length of the spring for which one spring extended by this length exerts one unit of force on the object to which it is attached. Two springs both connected to the object, pulling in parallel and both extended by this length would exert two units of force and so forth up to 10 units of force for 10 springs, extended by the standard length, all connected to the object and all pulling in the same direction. 2. Describe how you would use a force probe and the springs in (1) to develop a quantitative scale of force. Connect the springs to the hook on the force probe. Use these springs to calibrate the probe. One spring stretched to the predetermined length would correspond to 1 unit during the calibration procedure, 5 springs, in parallel pulled o the standard length would be entered as 5 units. The force probe should then be calibrated quantitatively to measure any force within its range in terms of the spring units. 3. What is meant by a proportional relationship? Is this the same as a linear relationship? Explain. “proportional” means that the dependent variable is a constant multiple, either positive or negative, of the independent variable. “Linear”means that the dependent variable is a constant multiple of the independent variable plus or minus a constant offset. 4. Given...
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...LAB REPORT 4 Hooke’s Law Objectives * To perform an experiment to measure the spring constant of a coil spring. Theory * Hooke's Law states that if the distortion of an elastic body is not too large, the force tending to restore the body to equilibrium is proportional to the displacement of the body from equilibrium. F = - k r where F is a restoring force, k is a constant of proportionality and x is the distance the object has been displaced from its equilibrium position. The minus sign signifies that the restoring force acts in the opposite direction to the displacement of the body from the equilibrium position. So, we can translate this formula into: F= KsX * If a body, which obeys Hooke’s Law, is displaced from equilibrium and released, the body will undergo “simple harmonic motion”. From the experiment, we can get the T that is one oscillation of the spring, so we can get KT by: KT=4π2Mt/T2 Procedures Way One * Set up the apparatus as illustrated. * Place 200 grams on the spring and record the position of the bottom of the weight pan along the meter stick. * Repeat the step above by using 400 grams, 600 grams, 800 grams and 1000 grams, record the positions of all these masses. * Computer the force on the spring F by using the formula F= mg * Plot a graph of force, F VS Position, x using the values of F and x in the...
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...earlier results. This shows that period of oscillations can be determined by length and gravitational acceleration, and doesn’t depend on mass. In our other activity, we measured the period of an oscillating mass connected to a spring. We had a hanging spring, and hung mass to the bottom of it, each time measuring the change in length of the spring from the time before. To find the spring constant, we used the masses added to calculate each of their elastic forces, by multiplying each by gravitational acceleration, then plotting them with their corresponding spring deformation, and the slope of that graph was the spring constant, k, which was 8.22 N/m. Using this value, we calculated the period of motion for the mass of 0.1 kg using a different given equation than the one before, obtaining a period of 0.69 seconds. To verify our results, we used the VideoCom to graph the spring as we placed 0.1 kg on it and then bounced it, then calculated a period from position, velocity, and acceleration vs time graphs by finding the distance between two peaks. With an average of these three periods of 0.86 seconds, we found our results were correct in calculating by hand the period of motion. This proved that if one knows the spring constant and mass of an...
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...Boeing 767-200 pasenger jet has a cruising speed of 870 km hr-1 at an altitude of 11900 m. At this cruising speed, its two General Electric CF6-80A engines exert a combined thrust of 390 kN. The frictional force of the air opposing the motion of the plane is A. 0 kN B. 390 kN C. 870 kN D. 1260 kN The following information refers to questions 2 to 10 inclusive. The circus has come to town and the principal attraction is Cleo, the human cannonball. There is a large compressed spring at the base of the cannon as illustrated below. It is this spring that will propel Cleo out of the cannon through the air to the safety net. The force-compression graph for the spring is also shown. [pic] [pic] Question 2 What is the spring constant for the spring inside the cannon? Question 3 How much energy is stored in the spring when it is fully compressed by 8.0 m'? Question 4 Cleo has a mass of 50 kg. Calculate Cleo's velocity just as she leaves the mouth of the cannon, assuming that the spring has transferred all of its energy to Cleo at this point. Question 5 The length of the cannon is 8.0 m. What is the net average force exerted on Cleo while she is travelling through the cannon? Question 6 What is Cleo's average acceleration while she is travelling through the cannon? The cannon makes an angle of 450 with the horizontal as shown in the diagram below. [pic] Question 7 How far (horizontally) from the mouth of the cannon must the centre of the safety net be...
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...in the springs once weight has been applied relating to Hooke’s Law. Key Results: When adding more force to the springs, the springs stretch further to the ground, then bounce further upward when released. The more force applied the more the restoring force will be. The restoring force is in the opposite direction from the displacement of the spring. The restoring force and the displacement depend on how hard or soft the spring is. The harder the spring the more difficult it is to stretch or bounce. The softer the spring the easier it is to stretch or bounce. The k of Spring 1 is 30 cm. When 50 grams were added the measurement dropped to about 35 cm when the spring stopped moving. When 100 grams were added the measurement dropped to 40 cm. When 250 grams were added the measurement dropped to 55 cm. The Effects of Mass: The larger the mass the longer the spring. To determine this effect I started by adding the smaller mass to the first spring and watched until it stopped its movement. I then proceeded with the same procedure with the medium mass, then finished with the larger mass. The Effects of Gravity: To determine the effects of gravity I first set the friction and softness back to the constant levels. When there was no gravity the springs were all at the constant level as if nothing were hanging on the springs at all. As the gravity increases the further the springs would stretch depending on the mass. When changed to the Moon the springs stretched...
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...Front Cover The Vibrating Spring - Experiment #02 Many objects in the real world have a frequency at which they vibrate. In modern engineering it is required to take this into consideration when designing them. There are many variables which could affect this frequency, therefore test are required to be conducted to see what these variables are and how they affect the vibrations the object undergoes. A vibration occurs when there is an oscillation about an equilibrium point. A good example for where oscillations occur is in a car’s suspension. The suspension takes a hit when a car goes over a bump or into a pothole. The springs in the suspension then oscillate and make the car “bounce” up and down. This is when the shock-absorbers kick in and damp the oscillations to make the car level again. The variables that could change the oscillations which the suspension undergoes could be the diameter of the springs or the number of coils. This would have been tested when the suspension was designed to make sure the car is safe and comfortable for the driver. The picture on the right shows a typical suspension that would be installed on a car. The coils can be clearly seen in the picture as well as the shock absorber in the centre which damps the oscillations. In the experiment which has been conducted here the vibrations of certain springs have been observed to see what variables affect the frequency at which they oscillate. The relationships between these variables and their...
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...done against gravity. The work done by the moving force is equal to the change in gravitational potential energy if the object is moving at a constant speed. In order to move an object up an inclined plane, work must be done against the gravitational force AND friction on the inclined plane. The work done by the pulling force will be equal to the negative work done by friction, if the object is moving at a constant speed. Objective: To verify the law of conservation of energy Materials: Inclined plane, smooth wood block, spring scale, meter stick Set up: [pic][pic] Procedure: 1. Make sure the incline plane and block are clean. 2. Set the incline so that the block just slides down. Measure the length of the incline and the height of the incline. Record in the data table. 3. Place the block at the bottom of the incline. 4. Hook the spring scale to the block and pull the block up the plane at a constant velocity. Read and record the force measured by the spring scale. (This force is equal to the component of the weight directed down the incline plus the frictional force acting on the block down the incline) [pic] 5. Place the block at the top of the incline with the spring scale attached. Let the block slide down the incline at a constant velocity. Read and record the force measured by the spring scale. (This force is equal to the component of the weight directed down the incline plane minus the frictional force directed up the incline plane) ...
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