Handout Newton\'s Second Law and Friction (formerly Newton’s Laws) PDF

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Handout Newton's Second Law and Friction (formerly Newton’s Laws)...

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Physics 244

Newton's Second Law and Friction (formerly Newton’s Laws) Introduction In this laboratory you will test a few aspects of Newton's Second Law and friction. In Part I, you will use a fan to accelerate a dynamics track cart and use the data from a combination of different masses added to the cart to experimentally test Newton’s Second Law. In Part II, you will observe the magnitude of the frictional force on an object at rest as well as the force of kinetic friction once that object has been brought to a constant velocity. This will be done indirectly by observing the force needed to pull an object over a rough surface at constant velocity.

Materials Part I: dynamics cart and track, fan, motion sensor, force sensor, set of masses, Data Studio, Excel Part II: friction carts, dynamics track, force sensor, set of masses

Reference Giancoli, Physics 6th Edition: Chapter 4, sections: 2,4,5,6,8

Theory Part I: Newton's Second Law is written mathematically as   F  ma

(1) From this equation we see that two things affect the acceleration of a cart: the applied force and its mass. For example, a more massive cart will require a greater force in order to achieve the same acceleration as a less massive cart. In this experiment, the force used to accelerate the cart is applied by a fan motor. When the motor is turned on, the blades of the fan exert a force on the air, which in turn exerts an equal and opposite force on the blades in the opposite direction (remember Newton's Third Law?) It is the reaction force of the air on the blades of the fan (which is firmly attached to the cart) that propels the cart forward. By measuring mass and acceleration, one can calculate the applied “force” under a number of conditions. Part II: There are two classes of frictional forces, those for objects at rest (static friction) and those for moving objects (kinetic friction). The force of kinetic friction on a moving object acts in the direction opposite to the velocity of the object. The magnitude of the force of kinetic friction is given by F fr (moving )  k FN

(2)

where  k is the coefficient of kinetic friction and FN is the normal force. In this experiment you will study friction on objects moving horizontally and the normal force is equal to the weight of the object mg. Thus, (3) F fr (moving )  k mg , which can be solved for k as:

k 

F fr (moving )

(4)

mg

In the static case, things are slightly more complicated. Similar to Equation 2, we can write: F fr (max, static)   s mg

.

(5)

This however gives the maximum force that static friction can generate (in resisting another force trying to move the object) before the object starts to slip and move. In general, the force generated is less than this, i.e. F fr  s mg . We can solve Equation 3 for the static coefficient of friction  s ;

s 

F fr (max, static) mg

.

(6)

Procedure Part I: Measuring mass and acceleration for a cart.

1. Make sure the track is level. You can check by making sure that the cart does not roll towards one end or the other spontaneously. 2. Measure the mass of the cart with the fan, convert it to kilograms and record it in Excel. Record in kilograms so that when you calculate the force the results will be in Newtons. You should generate a table with the following format. The total mass is the mass of the cart plus the mass added to the cart. Mass Added (kg) 0.000 0.200 0.400 0.600 0.800

Total mass, m (kg)

Acceleration, a (m/s2)

m  a (kg-m/s2=N)

3. Connect the motion sensor to the Science Workshop interface and Create an Experiment in Data Studio. You want to select Motion Sensor from the Sensors menu. Create a graph of Velocity vs. time.

Figure 1- Dynamics Cart with Fan. 4. Set the cart on the track at the end farthest from the motion sensor. Orient the cart so that the fan propels air away from the motion sensor (propelling the cart toward the motion sensor). 5. One student should turn the fan cart on and hold the cart in place while the other student presses Start to begin collect data in Data Studio. You may want to delay releasing the cart for a second in order to make sure you get all the data. 6. Release the cart, being sure to catch the cart BEFORE it hits the motion sensor, then hit Stop in Data Studio. 7. Highlight the points on your graph that follow a straight line (the slope should be negative because the cart is accelerating towards the motion sensor). Do NOT include the end points of this line segment in the data (those values may be affected by forces your hands apply in releasing and stopping the cart.) 8. Using the Linear Fit tool, measure the slope of the velocity graph and record this value which is the acceleration in the table you made in Excel. 9. Repeat steps 4-8 using the following masses added to the cart: 0.2 kg, 0.4 kg, 0.6 kg and 0.8 kg. If you can, include all the velocity data on the same graph. Secure the mass to the cart with tape if necessary. Remember to record the total mass in kilograms including the mass of the cart! 10. Once you have recorded all of your mass and acceleration values, calculate the mass times acceleration of the cart during each run. Newton’s Second Law predicts that these “force” values should be constant within uncertainties since the push of the fan is constant? 11. Calculate the average of these values and their standard deviation. Discuss. Is there any trend to the data?

12. Sample Calculation Include a sample calculation of "force" from Part I. For the error propagation, estimate the uncertainty for the mass; the statistical uncertainty for the acceleration is given by the uncertainty for the slope of the graph but you should add in a systematic uncertainty of about 3%. Use the resulting uncertainty to determine whether your calculated results agree with expectations.

Figure 2. Graph of absolute value of force sensor vs. time. Data recording was started several seconds before the experimenter began to pull on the cart.

Part II: Friction. 1. Connect the force sensor to the Science Workshop Interface and drag the Student Force Sensor icon to the input. Create and plot a graph of Force vs. time. 2. The force sensors can have problems so you need to be careful with your measurements. It is necessary to press the “tare” button when there is no force being applied to the force sensor so that it will have the correct zero. After you have tared it, test your force sensor by attaching a 0.200 kg mass to it hanging vertically. The force sensor should read approximately -2.0 N since weight = mg. The minus sign comes from the fact that the force sensor gives a negative value when you pull on in. When working with the force sensor you may need to take the absolute value of the force depending on the coordinate system you are using. If your force sensor doesn’t give the correct reading, you may need to replace it.

3. Measure the mass of the friction cart with the cork bottom and add 500 g to the cart. Connect the cart with cork on the bottom to the force sensor. Place the cart on a flat part of the dynamics track 4. Press Start in Data Studio, press tare and gradually begin pulling the cart with as constant velocity as possible. Since static friction is greater than kinetic friction, the force should drop once the cart has started to move. 5. Drag the friction cart a short distance along the dynamics track while maintaining a very low constant velocity. 6. Press Stop. If you were successful in maintaining constant velocity the force should remain constant. If the force increases or decreases at points on the graph it may be because the cart's velocity was not constant for that period of time. Your graph should look as much as possible like the one in Figure 2, but your data will have negative values because the force sensor yields negative values if you pull on it. It may take several tries to produce good data. Record data until it reaches a constant value. 7. Select a portion of the graph with relatively stable data and determine the average force over that time. (Highlight the data of interest then click on the  icon and select Mean.) Record the mean into your spreadsheet in Excel. 8. Do NOT erase the data from the graph; so you can compare it with subsequent trials with larger masses (let Data Studio overlay the successive graphs). 9. Repeat steps 3-7 with added masses of 1 kg, 1.5 kg and 2 kg. Observe the trend between kinetic friction (which directly opposes the applied force that keeps the cart at constant velocity) and the normal force (equal to the weight of the cart because it is on a horizontal surface.) 10. In Excel, calculate the normal force making sure to include the mass of the friction cart. 11. Create a graph of | Ffr | vs. FN . Is the graph linear? The slope of the graph should be the coefficient of kinetic friction for cork on aluminum. Calculate k . See Equations 2 through 6 above for reference. 12. Try to make a rough estimate of the coefficient of static friction s from you data. This is usually very difficult since the bump labeled Maximum Static Friction Force in Fig. 2 is usually not as clear as shown in that graph....