Physics Lab 4

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Lab 4 Frictional forces

Experiment objectives: 1. Apply the frictional force formula 𝑓 = 𝜇 ⋅ 𝑁 to determine the kinetic and static friction

coefficients 2. Distinguish the difference between static and kinetic friction 3. Conduct uncertainty analysis to determine the quality of measurements 4. Cultivate the habit of keeping all experimental data in a well-organized manner 5. Draw result-based conclusion

Experiment introduction:

Frictional force

Frictional force exists in many situations, and has a huge impact on our daily lives. The study of

frictional force involves a deep understanding of physics, material science, mechanical engineering,

etc. For students in an introductory physics course, who do not have all the necessary background

knowledge, a simplified model is presented. In this model, there are two types of frictional forces,

static, 𝑓s, and kinetic, 𝑓k.

For an object in motion, the kinetic frictional force 𝑓k on the object points in the direction opposite

of the relative motion at the contact surface, and has a magnitude given by Equation (1)

𝑓k = 𝜇k ⋅ 𝑁 (1)

where 𝜇k is the coefficient of kinetic friction, 𝑁 is the normal (perpendicular) force at the contact

surface.

For an object with a tendency to move, but not actually moving, for example a crate remaining

stationary on a loading ramp, the static frictional force 𝑓s on it points in the direction opposite to the

other forces that cause the tendency of motion. Please note that unlike the value of 𝑓k, the magnitude

of 𝑓s does not have a single value; instead, it exists in a range given by formula (2),

0 ≤ 𝑓s ≤ 𝜇s ⋅ 𝑁 (2)

where 𝜇s is the coefficient of static friction, 𝑁 is the normal force at the contact surface. The maximum

value of 𝑓s, often referred to as 𝑓s, max = 𝜇s ⋅ 𝑁, is of particular interest, because, to move a stationary

object, one must apply a force to overcome the maximum static friction force first.

Please note that the values of the two friction coefficients, 𝜇s and 𝜇k, depend on the materials in

contact. For most materials, 𝜇s and 𝜇k have different values, and usually 𝜇k < 𝜇s. It is generally

believed that, for any given contact materials, the values of 𝜇s and 𝜇k are constant.

However, the constant coefficients are only believed to be constant for the sake of the simplified

version. In reality, many other factors can also affect the coefficients.

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Figure 1 depicts both the static and the kinetic friction force when a stationary block is pulled into

motion. At first, the static friction force 𝑓s builds up to balance the increasing pulling force and keeps

the block at rest; after 𝑓s reaches its maximum value 𝑓s, max, it cannot balance the still increasing pulling

force anymore; the block starts moving, and the static friction force now becomes the kinetic friction

force 𝑓k. It is evident that 𝑓k has a value smaller than 𝑓s, max. It is also evident that 𝑓s has a range of

values, while 𝑓k has approximately a single value.

Figure 1: Friction vss time figure.

Experiment Procedures

In this experiment, you are expected to perform the following steps in order to calculate the static

and kinetic friction coefficients.

1. Use a force sensor to SLOWLY drag a wood block into motion on a piece of special paper. The block must have its largest wood surface in contact with the paper. The force sensor will record the friction force vs time data. Please make sure the dragging force is parallel to the table surface

2. Change the normal force by adding various masses on top of the block 3. Repeat step 1 for the new normal force due to the changed mass 4. Repeat steps 2 and 3 for a total of 4 different masses 5. Read the maximum static friction force 𝑓s, max and the mean kinetic friction force 𝑓k of each

data run, then calculate the static and kinetic friction coefficients for each data run.

Please refer to the following images for more instruction of equipment setup and optimization.

Static friction force 𝑓s

Kinetic friction force 𝑓k

Maximum static

friction force 𝑓s, max

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Exploration notes:

The figure below shows the equipment needed for this experiment.

1. The metal bar can be used to add additional weight on the wood block.

Two things need attention when using a force sensor:

1. Make sure the hook on it is slightly loose. Tightened hook often leads to wrong reading.

2. Before each measurement, a force sensor must be zeroed by pressing the ZERO button with no force on its hook.

Experimentation Grade (30 points):

Inform your instructor once you confidently finish all experiment procedures. Your instructor will

assign your experimentation grade using the chart below.

Item 0 points 6 points

Data organization All data are randomly scattered. All data needed for calculation are recorded and organized in Excel for easy reading.

Sample force vs time curve

No screenshot of force vs time curve is attached.

A screenshot of the best force vs time curve is attached in the Excel sheet.

Friction coefficient calculation

Friction coefficients are calculated by hand.

Both the static and kinetic friction coefficients are calculated using Excel.

Significant figures The processed data are reported with incorrect significant digits.

All friction coefficients are recorded with the correct significant digits.

Units Units are missing for all quantities. Proper units are included for all physics quantities.

Wood block

Metal bar

Force sensor

Special paper