L03 The Coefficient of Static Friction 1

Pre-Lab Exercises Full Name: Lab Section: Hand this in at the beginning of the lab period. The grade for these exercises will be included in your lab grade this week.

1. A box of mass m is resting on a flat table. There is an applied force P and a static friction force acting on the block shown below. The coefficient of static friction between the box and the table is µs. Write Newton’s 2nd Law for both the x and y directions.

2. Write an equation for the magnitude of the static friction force in terms of the

block’s weight mg.

3. If the applied force just causes the block to budge, then the static coefficient of

friction is µs max and the applied force can be labeled Pmax. Using Fnet = ma = 0, what is the relationship between µs max and Pmax ?

4. What is the formula for calculating percent difference (difference between two measured quantities: x1 and x2)?

5. What is the formula for calculating the standard deviation of an entire population of quantities?

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The Coefficient of Static Friction

Full Name: Lab Partners’ Names: Lab Section: Introduction: The purpose of this laboratory experiment is to investigate the property of friction as it applies to two objects in contact and at rest with respect to each other. Friction is a highly complex phenomenon but can be simply approximated by assuming the quantity called the coefficient of static friction remains constant regardless of the mass of the object. As always, be sure to complete all bold-faced items, as they will be graded. The fact that there are fewer items to grade in this exercise means that each one will, of course, be worth more points. Equipment: Science Workshop interface Dynamics Track Dynamics Cart Force Sensor Bubble Levels Friction Boxes Masses Balance (500 grams +) Procedure:

1.1 Make sure the Science Workshop interface is connected to the computer. Turn on the interface first and then turn on the computer. This may already be done for you.

1.2 Open Pasco’s DataStudio® (icon should be on the desktop). 1.2.1 Select “create experiment” 1.2.2 Follow the instructions. Click any channel on the interface icon

and choose Force sensor and double click it. Make sure the lead goes to the correct analog channel on right as indicated.

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1.2.3 Under the Measurement tab, set the Sample Rate to 50. This is the frequency with which the sensor will take force readings.

1.2.4 Close the Experiment Set Up window.

1.3 Open a graph for your data. Level the track using the bubble level and the leveling screw.

Step 2.4 Step 2.9 2. Taking Data:

2.1 You can connect a rubber stopper to the force sensor to measure pushes or connect a hook to measure pulls. The sensor will record data from –50N to +50N with a pull on the hook measuring as a negative force and a push on the stopper measuring as a positive force. Connect the rubber stopper if it is not already connected.

2.2 Connect the force sensor to the dynamics cart using the small Phillips head screwdriver. Measure the mass of the friction box and masses provided. 2.3 Reset the force sensor to zero by pressing the button on the side labeled “tare” while making sure the force sensor is not touching anything. Do this between every trial. 2.4 Place the dynamics cart onto the dynamics track and place the plastic-bottomed friction box with the “flat” side (as opposed to the one with the small hook) facing the force sensor. You will have to offset the friction box slightly so that the rubber stopper will press against the box. 2.5 Place a black mass into the friction box. 2.6 Push on the plastic-bottomed friction box ten times with the force sensor/dynamics cart as follows: Apply a constantly increasing force P to the friction box. You will notice that although the box does not move, the force sensor is detecting an increase in the push on the button. At a certain point the box will “break”free and begin to move. At this point you have just exceeded the maximum static friction force which is equal to Pmax. Stop pushing at this point and you will see a severe drop in the graph. (See above graph for an example.)

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2.7 Click on the the smart/xy-tool icon and drag the icon that appears over ten of the peaks on this graph. You will see an (x,y) pair for the data point you have selected. Record the force values for these ten peaks in a chart in Excel. See the table below for an example. 2.8 Add another mass to the friction box and repeat steps 2.6 and 2.7, recording the values in your chart. 2.9 Now push on the friction box ten times from the other side with the two masses in it. You will see a plastic hook that you will need to push on with the force sensor. Do not simply rotate the friction box! Take the cart and place it on the other side of the friction box. Record this force data as well.

2.10 Repeat steps 2.3 through 2.9 for the felt and cork bottomed boxes.

3. Analyze the data:

3.1 Print one graph that you collected, along with titles and axis labels. 3.2 In Excel calculate the average max force of friction and the standard deviation

for each series of 10 pushes. Create an additional columns in your chart for your calculation. Click on the box that you want to contain Fmax avg for your first data run. Now enter the equation =AVERAGE(1st Fmax:10th Fmax) in the equation line up top, just like you did in the last lab. NOTE: Actually put in the correct box location for 1st and 10th Fmax. For example: (B2:K2). Create an additional column in your chart for calculating the standard deviation of the max forces using the equation =STDEV(1st Fmax:10th Fmax). 3.3 Calculate the coefficient of static friction and its standard deviation using Excel. Make sure your values for µ and standard deviation are recorded in your chart.

Material: Plastic

Direction # of Black Mass Pmax Pmax Pmax Pmax

Average Pmax

Standard Deviation

Masses (kg) (N) (N) (N) (N) (N) Pmax (N) Flat 1 Flat 2 Hook 2 Material: Felt

Direction # of Black Mass Pmax Pmax Pmax Pmax

Average Pmax

Standard Deviation

Masses (kg) (N) (N) (N) (N) (N) Pmax (N ) Flat 1 Flat 2 Hook 2 Material: Cork

Direction # of Black Mass Pmax Pmax Pmax Pmax

Average Pmax

Standard Deviation

Masses (kg) (N) (N) (N) (N) (N) Pmax (N ) Flat 1 Flat 2 Hook 2

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3.4 Print out a copy of your chart, complete with all data runs and average values of force and static coefficient of friction. Questions:

1. What is the percent difference between the coefficient of static friction for the flat side of the box with one mass and for the flat side of the box with two masses? Calculate the percentage difference for the other two surfaces. 2. How did you expect an increase in mass to affect the coefficient of static friction? Is the effect of increased mass large compared with the standard deviation? If so, what would be a physical justification for a difference in µ when the mass is increased? 3. How does the type of material on the bottom of the box affect the coefficient of static friction? 4. Does the coefficient of static friction seem to depend on the direction with which you push on the box? Why or why not? In answering this question you should consider whether the effect is large compared with the standard deviation.