44 Force extension characteristics for a spring / elastic material

Transcription

1 Sensors: Loggers: Force, Motion Any EASYSENSE Physics Logging time: SnapShot 44 Force extension characteristics for a spring / elastic material Read If a spring or any elastic material is being used in a machine we need to know the following: The relationship between the stretching force and the extension. The spring constant if the relationship is linear. The work done in stretching the spring / elastic material i.e. the energy stored when it is stretched. The following procedure and analysis may be used for a spring or an elastic material. The instructions supplied will be for use with a spring. Draw a sketch graph for the results you would expect to get when increasing force and measuring the extension of the spring. What you need 1. An EASYSENSE logger.. A Smart Q Motion sensor with the range set to distance (metres) 3. A Smart Q Force sensor 44-1 (V)

2 4. Springs (steel, copper, plastic), elastic. A spring of K ~7 N/m would be ideal for this work. The spring supplied with the Force sensor is for masses up to 5.0 kg and will not be suitable for small mass carrier systems. 5. Masses and mass hanger. Masses of 100 g weight each would be ideal. The masses used will depend upon the spring characteristics. 6. A small screwdriver to tare the Force sensor. 7. Retort stand, boss head, clamps. 8. G-clamp or similar to clamp the retort stand base to work surface. What you need to do 1. Assemble the apparatus as shown in the diagram.. From the EasySense software s Home screen select SnapShot. 3. Select Test Mode (Tools menu), zero the Force sensor with the unloaded spring attached. A small screwdriver inserted into the slot on the end of the tare control knob is useful for this procedure. 4. Add masses to load and unload the spring several times in stages. Check with your teacher the maximum load that you can safely use with the spring. Do not exceed this load or the spring will become permanently damaged. 5. Check that the Force sensor is still zeroed correctly, and adjust if necessary. 6. Click on the Start icon to begin logging. 7. Hold the mass carrier in position on the unstretched spring. Click on the graph area to record the first value of force and distance (force = zero). 8. Let the spring hold the carrier. When the readings are steady click on the graph area to record the second value. 9. Continue adding masses and recording the values until you have at least 6 readings. You will need 10+ readings if you are expecting a curve e.g. with elastic. Results and analysis (1) Force vs. Extension Characteristics (F vs. x) You need to calculate the Extension of the spring. Use the Post-log Functions (Tools menu). The distance measured in the experiment is the distance from the Sensor not the length (extension) of the spring. The function that is applied calculates the extension of the spring and corrects to give the increase in extension with the force applied. Use the following values in the function wizard 1. Select the Formula function ax + bx + c. Make x = the Distance data 3. Use the following values for a, b and c a = 0 b= -1 c = distance when the force = 0 4. Name = Extension 5. Unit = m. 6. Click on Finish to create the new data. To plot Force vs. Extension (F vs. x) Select Options Select Graph type as Line Graph Click on the X-Axis tab and select x - axis as Channel. You need to produce a graph of axis F vs. x. For a steel spring the graph should be a straight line and you need a line of best fit. Use Tools and select Best Fit, use the Automatic option on the wizard that starts. Make sure you selected the correct channels for the x and y axis. A yellow line will be drawn on the graph; this will be the line of best fit for the data (V)

3 Identify the gradient of the line from the information supplied with the best fit. This is the Spring Constant k for the spring. k = N/m State clearly, and in detail, the relationship between force and extension for the spring you used. Results and analysis () Work vs. Extension characteristics The work done in stretching a spring = the energy stored in the stretched spring. Calculate the work done / energy stored in stretching your spring for 6 values of the extension. You can do this in several possible ways, including:- From, From F1 x + possibly using Excel. if the line goes through the origin. From the graph of F vs. x, and calculating the area under the graph for different values of x. State clearly and in detail, the relationship between force and extension of the spring you used. Choose which method you wish to use and then fill in the following table and plot a graph of work done against extension:- Extension, x (m) Area = work done (J) Questions 1. Compare the force-extension characteristics of a steel spring and a length of elastic.. A car spring has a spring constant of 5,000 N/m. How much energy is stored when it is stretched by 0.05 m? 3. The world record for a bungee jump was set by jumping from a helicopter attached to a 50 m cord. The cord stretched by 10 m in length. Assume that the extension of the cord is linear, and the jumper has a mass of 80 kg. Calculate :- a) The potential energy lost by the jumper at the bottom of his fall. b) The energy stored in the cord at the maximum extension = potential energy lost by the jumper. Calculate the stiffness of the cord. Extension Repeat the above investigation using materials that do not stretch in a linear way e.g. elastic or springs made from copper wire. Plot Work vs. Extension graphs, if the Force vs. Extension graph is a curve then the area under the graph can be calculated by counting squares (V)

4 Spring theory Many commercial springs have a compressive force that needs to be overcome before they start to get longer. The Force extension graph will look like graph 1 for such a spring. Graph 1 force extension graph for a spring with a compressive force. The relationship between F and x is linear of the form: F = + c When the spring is stretched from zero extension to extension x then the work done:- W = Average Force x Extension Inserting values from the graph:- From the graph, ( F F 1) x + F F + = 1 Substituting for F F1 + F + ) ( 1 Equation 1 F1 x + Shaded area on graph = area of rectangle + area of triangle 1 = ( F 1 x) + ( x ) 1 = F 1 x + which is the same as Equation 1 If the spring starts to stretch as soon as a force is applied then F 1 = 0 and: Equation 44-4 (V)

5 Hooke s law Nearly all materials used in construction are rigid. They retain their shape when a force is applied to them. The reason for the rigidity lies in the interaction of the molecules and atoms that make up the material. A stretching force (tension) tends to try to pull the atoms of the material apart. Usually the stretching is very small as the forces acting between the atoms are very strong. The interatomic forces prevent movement of the particles. A compression force is countered by the repelling forces between atoms. The atoms are pushed together but they also repel each other. The result of the forces acting on the material is to distort it in some way. If the force is a tension the material extends. Robert Hooke found that the extension of a material was proportional to the applied force. Studying springs he was able to construct a law describing the effect of the force. Springs are used in this type of experiment as they increase the effect, the same response to a force will be seen in a wire or rod but it will be much smaller. When a force is applied to a spring tensioning it (the spring) will respond by extending. Hooke s law states: "Extension is proportional to the applied force that causes it" i.e. Fα x putting the constant of proportionality k the equation becomes, F = k is the stiffness of the spring in N/m. It is the force needed to stretch the spring by 1 metre. k is also the gradient of the force-extension curve Elastic limit If we keep loading the spring the linear relationship between force and extension will no longer be a straight line. The point at which the linear relationship fails is the spring s elastic limit and marks the elastic limit of the spring. A spring that has gone past its elastic limit will be permanently distorted. If the stretching force is reduced back to zero the spring will be permanently distorted. The distorted spring will have "springiness" but its characteristics will now be different from the non distorted spring. The spring will obey Hooke s law but will be permanently stretched. Application By shaping the wire or the coil pitch, springs can be designed to react in a particular way. These designed springs are found in car suspension units, machine mountings and any other device that needs to be stabilised or have its vibration reduced. Compression When a spring is in compression the same proportional effect between force and size of the spring exists 44-5 (V)