Purpose: In this lab, you will make some basic measurements of friction. You wil

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Question

Purpose:

In this lab, you will make some basic measurements of friction. You will measure the coefficients of static friction between several combinations of surfaces using an inclined plane, and you will measure the coefficient of kinetic friction between two of the combinations of surfaces you used in the static friction part of this experiment.

Part 1: Static Friction

Theory:

The coefficient of static friction ms can be measured experimentally for an object placed on an inclined plane (a.k.a. ramp, a.k.a. hill). The coefficient of static friction is related to the critical angle qc for the ramp, at which the object just begins to slide. Using what we have covered in class, you can derive this relationship yourself! At this critical angle, static friction preventing the object from sliding down the hill is just exactly equal to the component of the object’s weight along the hill. If the component of the weight along the hill were just a little greater, it would overcome friction, and the object would start to slide down. The free body diagram for this situation will look like the figure sketched below. Use this diagram to find an equation that relates ms to qc.

FN = Normal Force = mg cos()

FF = s x FN = s mg cos()

Fx = m Ax = FGx - FF = ?

FGx = mg sin()

Hint #1: the angle q of the incline is the same as the angle between the normal force N and the weight mg. Why?

Hint #2: The weight mg can be broken into two components. One component is along the incline (WH). The other component is “pressing into the hill”, and is equal in magnitude to the normal force N. (This is an example of a situation where the normal force is not equal to the weight!) Remember that you need to use the normal force to calculate friction, since f=mN. Now calculate what the angle of the incline should be, so that the component of the weight down the hill is just exactly balanced by friction.

Equipment:

For this lab you will need to share the following ramps and blocks with other lab groups:

Ramps Blocks

Aluminum Aluminum

Particle Board Brass

Stainless Steel Plexiglass

Plastic Copper

Rubber

Steel

Wood

Experiment:

Test at least 5 different combinations of materials. Record the material of the block and the ramp for each combination.

1. Measure and record the length of the inclined plane you will be using. (This is the hypotenuse of the right triangle!)

2. Place the block on the plane and begin tilting the plane just until the point when the block begins to slide.

3. Measure the height of the raised end of the inclined plane at this point. (This is the opposite side of the right triangle!) You can calculate the angle from the measurements of the two sides.

4. Repeat the height measurement at least 3 times for each combination of materials. Record all the measurements in the table below. Then,

(a) calculate the angle from the measurements of the hypotenuse and opposite side you just obtained

(b) use the equation you derived above in order to calculate the coefficient of kinetic friction from the angle.

Block: wooden block Block: cooper

Ramp:particle board Ramp: particle board

Length of ramp: 0.61(m) Length of ramp: 0.61(m)

Height(m)

0.24

0.26

0.25

0.31

0.245

0.345

avg ms: ______ s : _______ avg ms: ______ s : _______

Block: aluminum Block:particle board block

Ramp: solide wood Ramp: solide wood

Length of ramp: 0.605(m) Length of ramp: 0.605(m)

Height(m)

0.15

0.23

0.16

0.165

0.16

0.195

avg ms: ______ s : _______ avg ms: ______ s : _______

5. Remember that in class we said that friction does not depend on surface area. You can easily test whether or not this is correct. Choose a block/ramp combination not already tested, and make sure the block is not a cube or cylinder. Place the block so that the side with the larger surface area is in contact with the board. Now measure the angle at which the block just begins to slide (by measuring the hypotenuse and opposite sides of the corresponding right triangle). As before, calculate the coefficient of friction from the angle you measured, using your equation. Repeat this process with the side of the block with the smaller surface area in contact with the board. Enter this data in the small tables below.

Block (larger end) : _________ Block (smaller end) :__________

Ramp: _______________ Ramp: ________________

Length of ramp: ______(m) Length of ramp: ______(m)

Height(m)

avg ms: ______ s : _______ avg ms: ______ s : _______

Part 2: Kinetic Friction

Theory:

You can calculate the coefficient of kinetic friction, mk, using a variation of the method you used for the coefficient of static friction. For the coefficient of kinetic friction, you can use the same free body diagram as the one drawn on the first page. But now, the combination of WH and the force of friction will need to add up such that the block will slide at a constant speed. Think of Newton’s first and second laws when you set up this equation. Derive a relationship between the critical angle and the coefficient of kinetic friction.

Experiment:

You can measure mk using a procedure similar to the one you used to measure ms. This time, just pick two combinations of materials. The combinations you pick for this part of the experiment have to be combinations you already used for the static friction part of the experiment, because the point is to compare ms and mk!

1. Measure and record the length of the inclined plane you will be using.

2. Raise the plane high enough for the block to begin moving. Begin lowering the plane just until the point when the block begins to slow down. (Alternatively, raise the board while tapping the block until block moves at a constant rate.)

3. Measure the height of the raised end of the inclined plane at this point.

4. Repeat the height measurement at least 3 times for each combination of materials. Record all the measurements in the table below. Then,

(a) calculate the angle from the measurements of the hypotenuse and opposite side you just obtained

(b) use the equation you derived above in order to calculate the coefficient of kinetic friction from the angle.

Block (from part 1) : _________ Block (from part 1) :__________

Ramp: _______________ Ramp: ________________

Length of ramp: ______(m) Length of ramp: ______(m)

Height(m)

avg mk: ______ s : _______ avg mk: ______ s : _______

Analysis:

Calculate the mean value and standard deviation of the coefficient of static friction that you measured, for each set of materials.

ramp/board

pair

Standard

deviation

(larger end)

(smaller end)

Calculate the mean value and standard deviation of the coefficient of kinetic friction that you measured, for each set of materials.

ramp/board

pair

Standard

deviation

Questions:

1. How do the values of ms compare to the values of mk? (Of course, you can only compare them for the same pairs of materials.)

2. Is the relationship between msand mk what you expected?

3. Of the two parts of the experiment, measurement of msand measurement of mk, which had more sources of error? What were some of the sources of error?

4. Could mk or ms ever be greater than 1? Explain why or why not.

5. Is the coefficient of friction the same as when the block was standing on its larger (or smaller) end?

6. Think about your results. Do they make sense when you consider your everyday experiences?

FN = Normal Force = mg cos()

Explanation / Answer

draw a freebody diagram of the block on the ramp just as its about to break free from static friction.

Note that the weight of the block is pointed down, but not directly perpendicular to the ramp. Also note that the normal force IS perpendicular and pointing away from the ramp. The force of friction is pointing up the ramp because it is opposing the block sliding down. If you pretend that the normal vector is your y axis and your ramp is your x axis, using trig, you can see that the angle the weight makes with the y axis is the same as the angle of the ramp itself.

since we know that the block is on the verge of moving, the static friction must equal the force due to gravity along the ramp.
so we have
NM= mgSin() where N is the normal force, M is the coefficient of static friction, mg is the weight(mass times gravity) and is the angle of the ramp/weight-to-y-axis.

using a little more trig, we can determine the normal force as well.

N= mgCos().

so you can substitute your now solved normal into the first equation and solve for the angle of the ramp.

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