PHY 101 Lab 3 Diverse Forces, Springs and Friction

Transcription

1 PHY 101 Lab 3 Diverse Forces, Springs and Friction Name: Partner: Partner: Goals: To explore the nature of forces and the variety of ways in which they can be produced. Characterize the nature of springs, investigate friction and the forces between tethered blocks. Materials: Computer-based measurement system Logger Pro Three Carts with two having attached force probes and a Sonic Ranger Spring scales Masses A variety of force-producing systems. Activity: 1. Exploring and characterizing forces You are already very familiar with some forces from last week s lab. However, there are many kinds of forces. There are a number of different force-generating devices or systems that you can bring back to your station to study (see the Appendix attached at the end). Be sure that your choices are as dissimilar as possible and do not include springs as they are reserved for activity 2. Your team should bring back one at a time, then fill out the lab sheet according to these instructions: a. Describe the kind of force. 1

2 b. How strong is the force? Can it reach hundreds of Newtons? A couple of Newtons? A fraction of a Newton? Less? You can use spring scales of different range or computerized force probe to explore magnitude of the force. Use small coil spring to probe the weakest forces (first see how much force is needed to stretch this coil out). c. What does that strength depend on? (for example: distance between something and another thing, velocity, mass, electric charge, weight, chemistry, amount of squeeze/stretch,...) Does the force depend on contact between things? d. What is the direction of the force? (for example: attractive, repulsive, against direction of motion, upwards, downwards, outwards,...) Note that by asking you to give the magnitude and direction of the force, we are asking you to characterize a vector. 1) Kind of force: Strength of force: What strength depends on: Direction of force: 2) Kind of force: Strength of force: What strength depends on: Direction of force: 2

3 2. Springs We all think of springs as coils of metal. A more general way to think of a spring is as something that changes the location of one of its ends when you pull or push on it, by an amount that depends on how hard you push or pull. Springs of the ordinary coil-shaped sort are at the heart of your spring scale. Here we want to explore other kinds of springs. For each spring, give a description, state whether it works in tension (by stretching) or in compression (by squeezing) or transversely (by moving sideways), and measure how far its end moves for a given force. Check whether it moves by twice as much when you give twice as large a force, and that it comes back to its original state when you remove all of the external forces. A spring that does this is said to obey Hooke's Law. As part of the characterization below since you have a force probe and you have a ruler you should plot an extension-force curve for each spring and plot it on the computer. To set this up go to Experiment/Data Collection of LoggerPro. Chose Events with entry. Enter Column Name as extension distance short name distance. Click on Collect. Click on the Keep symbol (the iris diaphragm) which is to the right of the green Collect button when the spring extension is at the desired extension distance. Then the force at that distance will be automatically entered associated with the extension distance that you will type in from reading the ruler following each Keep action. In this way collect all the needed values. Be sure to enter into the computer the actual distances in cm. Your instructor will show you the variety of springs to study. Spring 1 (tension) description and characterization as above: 3

4 Spring 2 (compression) description and characterization (Make an additional column and plot as an additional curve): Spring 3 (constant force) description and characterization: (Make an additional column in your data table and plot as an additional curve): CAUTION: ONLY PULL THESE SPRINGS TOWARD THE TABLE. DO NOT EXTEND MORE!!! Sketch all three extension force curves 3. Friction Use the cart with no mounting bracket. Unlike previous uses of the cart, this time turn the cart upside down, so that the wheels are pointing upwards. Put four rectangular weights (1 kg) on top of the cart to increase its mass. Tie a piece of string to the hook on the force probe, and tie the other end to a convenient spot at one end of the cart. 4

5 Set up Logger Pro with The Force Probe in CH1 and the Sonic Ranger set to record the movement of the Cart. Set up graphs of position vs time, velocity vs time, acceleration vs time and force vs time. Zero the tethered Force Probe. Get ready to move the cart by pulling on the force probe. The string should be stretched but no detectable force should be applied to it. Start collecting the data with the cart at rest. Start applying the force. Do it very gently so you can explore range of forces for which the cart is still at rest. If you can, make the force increase linearly with time. Once the cart starts moving try to maintain constant force and constant speed of the cart. Then suddenly increase the pulling force and make the object accelerate. Since this is going to be printed out, you may wish to repeat this experiment until it looks good. PRINT (or sketch) all four graphs to add to this report. Underline the print out indicate 1, 2, 3, 4 and 5 second marks on the time axes for each plot. When reading your graphs pay attention to where the zero on vertical axis is, and draw on your print out the moment or point at which there was a change of trend in the measured quantity. Identify on the print out of the graphs when the force was already applied but the cart was still at rest. Indicate this range by vertical bars on the force vs. time graph and label it Region 1. Mark the same time period on the other three graphs. The force we measured here is clearly not zero, but since the cart is at rest it has zero velocity and acceleration. Doesn t this contradict the F = ma law? Explain. What force F do you use in the equation F = ma? The new force, which came into play here, is called static friction. Draw a free body diagram for the cart and indicate the static friction force, fs, and the force exerted by the string on the cart, T. 5

6 Which force is measured by the force probe? Does static friction have a constant magnitude? Can static friction assume any value? Now on the print out of your velocity vs. time graph, indicate when the cart was moving with approximately constant velocity. Mark this time period with vertical bars and label it Region 2. Mark the same time interval on the other three graphs. Since velocity is approximately constant, the position vs. time graph should be linear and acceleration should be approximately zero. Check it with the computer. Again, the measured force is not zero but there is no acceleration. The force exerted on the cart, T, is balanced by the force of kinetic friction, f k. Unlike static friction force, kinetic friction force does have a constant magnitude independent of the force it opposes. Thus when T is increased fk cannot balance it and the object accelerates. Identify time interval on your graphs that corresponds to this of motion and mark it Region 3. We will now quantitatively investigate the force of kinetic friction. We can obtain magnitude of this force from the Region 2, since here, T = fk. Stretch a selection range on the force vs. time graph to cover the Region 2. Then go to Analyze menu and click on Statistics. Make sure that the selection bars don t disappear when you do that. Store the mean value of the force in this range (displayed in the superimposed box) in the table below. Remove 0.25Kg weight from the cart leaving 0.75Kg on the cart. Zero the force probe. Repeat the experiment. This time you just need to concentrate on obtaining motion with constant velocity ( Region 2 ). Stretch the selection range on the force vs. time graph for the Region 2, and obtain mean force value in this time interval. Store it in the table. Repeat with net 0.5 Kg and 0.25 Kg on the cart Finally, take the last weight off and repeat the measurement process for the cart alone. Remember to zero the force probe before taking data. 6

7 Object Cart with four rectangular weights (1 Kg) f k (N) Mass measured with a balance - m (kg) Coefficient of kinetic friction Cart with three rectangular weights (0.75 kg) Cart with two rectangular weights (0.5 kg) Cart with one rectangular weight (0.25 kg) Cart by itself Measure mass of the cart with and without weights using a balance and store your measurements in the table. Sketch below a graph of f k vs m. What kind of simple function could describe dependence of f k on m? 7

8 Complete the table by calculating coefficient of kinetic friction: µ k = f k / N. Here N is a normal force exerted by the track on the cart. Since the cart is not moving in vertical direction this force balances the weight of the cart: N=mg. (Include N and mg on your free body diagram). This coefficient should not depend on the force applied to the cart, mass of the object, nor the area of the surfaces that are in touch. It does depend on type of the surfaces that are at friction. Do the results for the coefficient roughly agree between the five measurements? Since static friction is not a constant force, coefficient of static friction is not defined as µ s = f s / N. You may have noticed that the maximal value of the static friction decreases with the mass of the object. In fact, coefficient of static friction is defined as µ s =(maximal f s ) / N. Coefficients of static and kinetic friction are usually similar but not identical. It is obvious that if they are not equal then, µ s > µ k. This can be observed as slight drop in the measured force as you transit from Region 1 (object at rest) to Region 2 (motion with constant velocity). Do you see the effect on the force vs. time graph that you copied to your report? If you don t try to take data again (cart with two weights on) concentrating on the moment when the cart starts moving, don t apply more force than needed to keep it in motion. Invert the cart and put it back on its wheels with four weights on top (1 kg). Measure coefficient of kinetic friction. Show your result here, and compare it to the value obtained before. 8

9 4. Force or tension between two pulled masses Suppose two connected carts are on a frictionless track, one with four rectangular weights (1kg) attached and one without added weights, but carrying a force probe to measure the tension between the carts. Suppose this pair of connected carts were pulled by application of a pulling force to one of them. The question is what would be the force between the two pulled carts joined by a force probe and would it depend on the order in which they are connected? Suppose we have a third cart with a mounted force probe which can be used to pull the other carts. This will enable us to provide a measured force F that pulls the three carts together. To be specific let m 1 be the total mass of the puller cart or carts if one is joined to the puller. Let m 2 be the mass of the cart or carts that are not connected directly to m 1. Of interest is the relationship between the pulling force F and the force between the m 1 and m 2 T when the pulling is of the heavier cart or alternatively the lighter cart. Would the inter-cart force T be F or some other value in each case? Make a free body diagrams of the single cart and the firmly attached puller and adjacent cart that can be considered as one cart and calculate your expectations for the ratio (F/T) of the puller force F to the tension T between the carts in terms of m 1 and m 2. 9

10 Try it. Use the cart with the tethered Force Probe connected to CH1 and hence, Force 1, as the puller F. You will be pulling the hook of its force probe along the track and the other end will be used to pull the pair of light and heavy carts (see figures in the Table below). The adjacent cart of the connected pair can be connected to it by the Velcro. The carts connected by the force probe can connected together with the aid of string. Use the cart with an attached Force Probe connected to CH2 as the lighter cart. Use the heavier 1 kg loaded cart without a force probe as the heavier cart. Set up LoggerPro so that Force 1 and Force 2 are displayed on the same graph, No other graphs are needed. Connect as in the figure on the left and pull the force probe hook of the puller cart pulling itself and the two trailing carts with the force F. Pull with as constant a force as possible, since you are not using the sonic ranger you can make use of the whole length of the track as the runway for your experiment. Practice a few times before collecting data by clicking the Connect TAB. Autoscale and on the Data tab click on Store the latest run. Now go the figure on the right the force and repeat as above. To analyze for each of the cases select the region with constant force and in the Analyze tab click on Integrate for all four cases and enter values for F and T in the table below. Then calculate the ratio of F/T and compare to that expected from your calculation and the known masses. Puller Heavy Light cart 1kg g0k Puller Light Heavy cart 1kg g F (Force 1) T (Force 2) Ratio of F/T Expected F/T from theory Create the appropriate graph of results and PRINT it out. 10

11 Appendix to Lab 3: Examples of Forces: 1. Muscles two opposed sets since force can only be applied with shortening the muscle 2. Weights 3. Tension in strings or ropes 4. Force between two magnets 5. Electrostatic force (two balloons, charged by rubbing on hair or on sweater) 6. Buoyancy (boat floating in water) 7. Air pressure (air pump and bicycle tire) 8. Air exhaust rocket (balloon) 9. Chemical bonds between layers of adhesive tape 10. Sliding friction 11. Air friction 12. Fluid friction 13. Friction from magnet-induced currents ( eddy currents ) 11