4-3 Static and Kinetic Friction Lab PDF

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4-3 Static and Kinetic Friction Lab of Algebra-based Physics I Lab...

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Static and Kinetic Friction Lab Purpose: To determine the relationship mathematically and graphically between the maximum forces of static and kinetic frictions and normal force of objects. Then determine the coefficients of static and kinetic friction for the surface used.

Apparatus: For this investigation the equipment used is as listed: Materials: 1. 2. 3. 4.

5.

Independent variable: Force, Dependent variable: Force of Friction

Friction Trays String Mass sets Computer with Logger Pro Lab Pro with dual range force sensor

Procedure: Part I Practice Pulling. 1. Measure the mass of the tray and record it in the data table. Record the type of surface on the bottom of your tray (plastic, cork, felt, etc.). 2. Connect the Dual-Range Force Sensor to Channel 1 of the interface. Set the range switch on the Force Sensor to 500N. Connect the interface to a laptop and start Logger Pro. 3. Open the file “12a Static Kinetic Friction” from the Physics with Vernier folder in Logger Pro. 4. Tie one end of a string to the hook on the Force Sensor and the other end to the hook on the tray. Place a total of 1 kg mass on top of the tray, fastened so the masses cannot shift. Practice pulling the tray and masses with the Force Sensor using this straight-line motion: Slowly and gently pull horizontally with a small force. Very gradually, taking one full second, increase the force until the tray starts to slide, and then keep the tray moving at a constant speed for another second. 5. Hold the Force Sensor in position, ready to pull the tray, but with no tension in the string. Click set the Force Sensor to zero.

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6. Click to begin collecting data. Pull the tray as before, taking care to increase the force gradually. Repeat the process as needed until you have a graph that reflects the desired motion, including pulling the tray at constant speed once it begins moving. Print or copy the graph for use in the Analysis portion of this activity. Part II Measuring Maximum Static Friction and Kinetic Friction In this section, you will measure the peak static friction force and the kinetic friction force as a function of the normal force on the tray. In each run, you will pull the tray as before, but by changing the masses on the tray, you will vary the normal force on the tray. 7. Remove all masses from the tray. 8. Click

to begin collecting data and pull as before to gather force vs. time data.

9. Examine the data by clicking the Statistics button, . The maximum value of the force occurs when the tray started to slide. Read this value of the maximum force of static friction from the floating box and record the number in your data table. 10. Drag across the region of the graph corresponding to the tray moving at constant velocity. Click on the Statistics button again and read the average (or mean) force during the time interval. This force is the magnitude of the kinetic frictional force. 11. Repeat Steps 9-11 for two more measurements and average the results to determine the reliability of your measurements. Record the values in the data table. 12. Add masses totaling 200 g to the tray. Repeat Steps 9 – 12, recording values in the data table. 13. Repeat for additional masses of 400, 600, 800 and 1000 g. Record values in your data table.

Raw Data: Mass of Plastic bottomed tray: 0.915 kg

Table 1 Peak Static Friction Mass

Trial 1

Trial 2

Trial 3

(kg)

(N)

(N)

(N)

0.915

0.2188

0.2818

0.2503

1.115

0.6946

0.7245

0.7844

1.315

1.165

1.070

0.9758

1.515

1.291

1.386

1.417

1.715

1.638

1.670

1.638

1.915

2.490

1.922

2.017

Table 2 Kinetic Friction Mass

Trial 1

Trial 2

Trial 3

(kg)

(N)

(N)

(N)

0.915

0.1608

0.1517

0.1672

1.115

0.4385

0.4376

0.4601

1.315

0.8400

0.7525

0.7842

1.515

1.007

1.024

0.9872

1.715

1.184

1.300

1.250

1.915

1.648

1.548

1.493

For the assembly of this lab we used a computer with Logger Pro, Vernier Lab pro with dual range force sensor, a plastic bottom tray, a string, and a mass set. We turned on the computer and opened logger pro. Under file we opened Physics with Vernier and then opened 12a Static Kinetic Friction. Then we connected the Lap pro to the computer with the data cable, and to the force sensor in channel one. Then we took the plastic bottom tray and weighed it on the scale to get the mass which is shown above as the mass of the plastic bottom tray. The scale read the mass to be 0.915 kg. Then we tied a string to the tray and attached it also to the hook on the force sensor. The force sensor was set to 50 N. We pulled the string tight but without tension so that we could zero the force on the sensor in logger pro. Then we began to collect our data. First we measured the force necessary to move the tray alone with no mass added to it. On Logger pro we hit the collect button and then started to slowly pull the force sensor just to the point that the tray began to move, and then once the tray was moving it was attempted to keep it at a constant speed as it moved across the table. The point at which the tray began to move is the max static friction which is recorded in Table 1 under raw data. This was repeated for three trials for each different mass. Then the point from where the tray was moving at a constant rate was recorded as the mean kinetic friction and entered in table two. We did this for three different trials for each different mass as well. **Note: mass of tray was added to each different mass (i.e. .200kg, .400kg etc…) to get the total mass.

Data Analysis: Static and Kinetic Friction – Part 1 (Force vs Time graph)

Force vs Time

For the Static and Kinetic Friction (Force vs Time) - Part 1 the dependent variable on the Y-axis is the Force needed to get the tray to move. The independent variable on the X-axis is Time it took to record the force to start the tray moving and keep it moving at a constant velocity. On the graph you see starting from the yintercept this represents the tray at rest. Then the line begins rising and then peaks at the top and begins descending. This is where the tray began to move. The line rising is the force acting on the tray acting against the friction to begin the tray moving. The peak is the maximum static frictional force it took before the tray began to move. Then the jagged line after the peak is showing the kinetic friction of the tray at a constant velocity. The max force statistic was used for the static friction which was recorded in Table 1. The mean force statistic was used to record the kinetic friction and entered in Table 2. Comparing the force needed to start the tray moving on the surface, and the force needed to keep it moving the graph shows that it takes a greater force to start the tray moving on the surface then it does to keep the tray moving at a constant velocity.

Table 3 Total Mass (kg)

Normal Force (N)

Peak Static Friction Trial 1

Trial 2

Trial 3

(N)

(N)

(N)

Average Peak Static Friction (N)

0.915

8.976

0.2188

0.2818

0.2503

0.2503

1.115

10.94

0.6946

0.7245

0.7844

0.7345

1.315

12.90

1.165

1.070

0.9758

1.070

1.515

14.86

1.291

1.386

1.417

1.365

1.715

16.82

1.638

1.670

1.638

1.649

1.915

18.79

2.490

1.922

2.017

2.143

Sample Calculations: Trial 1 + Trial 2 + Trial 3÷ 3 = Avg Ffr(s) 0.2188 + 0.2818 + 0.2503 ÷ 3 = 0.2503 N

mg = Normal Force 0.915 ×9.81 = 8.976 N

For Table 3 we first calculated the Normal Force by multiplying the mass by the Force of gravity (9.81 m/s2). Those value were recorded under the Normal Force on Table 3 for each different mass. Then to calculate the Average Peak Static Friction we added the three trials of Peak Static friction together and then divided it by three. Those values were recorded under Average Peak Static Friction for each different mass. The statistic for the max force was recorded for the trials for the Peak Static Friction.

Table 4 Total Mass (kg)

Normal Force (N)

Kinetic Friction Trial 1

Trial 2

Trial 3

(N)

(N)

(N)

Average Kinetic Friction (N)

0.915

8.976

0.1608

0.1517

0.1672

0.1599

1.115

10.94

0.4385

0.4376

0.4601

0.4454

1.315

12.90

0.8400

0.7525

0.7842

0.7922

1.515

14.86

1.007

1.024

0.9872

1.010

1.715

16.82

1.184

1.300

1.250

1.245

1.915

18.79

1.648

1.548

1.493

1.563

Sample Calculations: Trial 1 + Trial 2 + Trial 3÷ 3 = Avg Ffr(k) 0.1608 + 0.1517 + 0.1672 ÷ 3 = 0.1599

mg = Normal Force 0.915 ×9.81 = 8.976 N

For Table 4, to calculate the Average Kinetic Friction we added the three trials of Kinetic Friction together, and then divided the value by 3 to get the Average Kinetic Friction. Then the values were recorded under the Average Kinetic Friction on Table 4 for each different mass. The exact same values used for Normal Force in Table 3 were also used in Table 4. The statistic for mean force was recorded for each trial for the value of kinetic friction.

Static Friction vs Normal Force

For Static Friction vs Normal Force graph we used the values in Table 3 for our data to create this graph. On the y-axis is the Force of static friction measured in Newtons (N). We used the value from Table 3 under Average Peak Static Friction for the static friction for this graph. Then also in Table 3 we used the Normal Force values for the Normal Force on the graph which is showing on the x-axis. The formula for this graph is Ffr(s) = 0.1279N + (-0.3872) which represents a linear fit relationship between Force of static friction and the Normal Force. The meaning of the slope for this graph is the coefficient of static friction which is 0.1279. The

y-intercept represents the tray at rest on the surface. To obtain the coefficient of static friction you would divide the force of static friction by the normal force. The static friction is the resistance to the normal force to keep the tray from moving, and the coefficient of static friction represents the maximum resistance.

Kinetic Friction vs Normal Force

For Kinetic Friction vs Normal Force graph, we used the values in Table 4 for our data to create this graph. The y-axis is showing the Force of Kinetic Friction measured in Newtons (N). The x-axis is showing the Normal Force also measured in Newtons (N). The Average Kinetic Friction values in Table 4 was used for the Kinetic Friction on this graph. The Normal Force values in Table 4 were used for the Normal Force on this graph. The formula for this graph is Ffr(k) = 0.1403N + (-1.078) which represents a linear relationship between Force of Kinetic Friction and Normal Force. The meaning of the slope for this graph is the coefficient of kinetic friction. The y-intercept for this graph would represent the kinetic friction at a constant speed. The force of kinetic friction depends on the normal force, and on a horizontal surface the normal force is equal and opposite the weight of the object. Being that the force of kinetic friction was moving at a constant velocity then the force of kinetic friction equals the normal force. So yes the force of kinetic friction is dependent on the

weight of the tray. For masses on an incline the normal force is less than the weight so the force of kinetic friction would not be dependent on the weight of the tray. The coefficient of kinetic friction is not dependent of the weight of the tray it is dependent on the surfaces of the two objects sliding against each other.

Conclusion: “Normal force is when a contact force acts perpendicular to the common surface of contact.” (Giancoli’s Physics Principles with Applications (7th ed.), section 4-6, page 84.) Force of Static Friction is the force necessary to get an object moving on a surface. Force of Kinetic Friction is the force needed to keep and object moving on a surface. In this lab the purpose is to identify the relationship between normal force and the force of static and kinetic friction, and to determine the coefficient for the force of static and kinetic friction. For the first part of the lab we determined the average force of static and kinetic friction by pulling on a force sensor attached to a tray across a smooth surface. We recorded three trials for each different mass plus the mass of the tray. Then for the second part of the lab we graphed Force of friction vs Normal force for static and kinetic friction. Graphically the results show to be a linear relationship between force of friction and normal force. Mathematically to determine the coefficient of friction we used the formula µ(s,k)=Ffr/N. The µs is equal to 0.1279. The µk is equal to 0.1403. Comparing the Force of Static Friction and Kinetic friction it shows that the Force of Static Friction is greater than the Force of Kinetic Friction. The y-intercept for the Static Friction vs Normal Force should be 0 but the graph shows the y-intercept to be -0.3872 which would indicate an error. This error may be due to not correctly setting the force sensor to zero. Measuring the weight of the tray on the scale caused greater uncertainty because the scale did not balance exactly at zero. There was error in recording static friction when the tray was moving prior to hitting collect on the logger pro. There was also error in recording kinetic friction because it required the tray to move at constant velocity but using the force of my hand pulling the sensor is not exactly accurate in creating constant velocity....