Phys Lab

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Physics 161 Lab 3, Static and Kinetic Friction Objective To test a theoretical model of friction and experimentally determine which attributes of objects control their frictional interaction in both static and kinetic situations. Turn in There is no preliminary survey for this lab. The lab exercise for this lab will be due in one week after posting. The lab exercise can be accessed on Canvas by clicking the “Assignments” link on the front page. Background, Part A: Coefficient of Friction Theory We will restrict our discussion of friction to refer to a certain force that acts along the surface between two objects in contact. Consider the block on the floor as shown in the drawings to the right. All forces acting on the block are shown in Fig. 1. If the block is stationary, then the forces must all balance each other out. The “normal force” exerted upward on the block by the floor must balance the force of gravity (exerted by the Earth) acting downward. When a force by some external agent is pulling the block to the right, but if the block doesn’t move, there must be a force of resistance acting to the left. This is the friction force, which has its origin in the interaction between the atoms of the block and those of the floor. While the friction force is acting at all points of contact between block and floor, we generally lump them together into a single force vector (arrow) as shown in Fig. 2. The friction force can act in any direction along the contact surfaces, but it always will act according to a certain rule: The friction force acts so as to try to maintain the surfaces in static contact. Thus if the force Fext turns around and acts to the left, the friction force exerted by the atoms at the contact surfaces will turn around (Fig. 3) and act to the right to oppose the attempt by Fext to move the block. For a sliding object, the friction will act so as to try to stop the relative motion between the surfaces. This works even when pulling a tablecloth out from under a vase (Fig. 4). Last, the friction force can even be zero if it does not have to oppose any motion or oppose any external forces. If a block sits on a horizontal surface, you cannot tell whether the block is glued to the floor or greased so well that it will slide off at the slightest touch.

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DEFINITIONS: Static friction acts between two surfaces that are not moving relative to each other (that is, they are static). The static friction force can have any value between zero and a certain maximum at which point the friction can be overcome and one object will start to slide across the other. Then the friction force is no longer static. Kinetic friction acts between two surfaces that are sliding past each other.

The magnitude of the friction force is often related to the magnitude of the normal force. If you add another identical block, the table must double the normal force to support two blocks instead of one. In such a case the maximum limit to the static friction roughly doubles, meaning that it is roughly twice as hard to pry the blocks loose. If the blocks are already in motion, the kinetic friction will be roughly double what it was with one block. The term “roughly” has been inserted several times to underscore the fact that the friction force defies an exact theory. Its value is neither predictable nor even reproducible, though approximate characterizations are possible. The coefficient of kinetic friction, µk, is defined as a ratio of the magnitude of the kinetic frictional force to the normal force:

The coefficient of static friction, µs, is trickier because the static frictional force can have any value between zero and some maximum. An object can only be set in motion when its maximum static frictional force is overcome. The coefficient is also defined as a RATIO, but of the maximum static frictional force to the normal force:

Remember, the coefficient is not the force itself, but represents a fraction of the normal force. When µk = 0.30, then the kinetic friction force is 30% of the normal force. Note that for any two materials in contact, these coefficients of friction are constant in our simple model of friction. This means the frictional force does depend on the normal force, but cannot depend on other factors, including the area of contact between the two surfaces. Different materials will have different coefficients of friction.

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µk = Fkinetic FN

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µs = Fs,MAX FN

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Equipment

• Wooden block with eye bolt • Felt • Spring scale • Washers • Cell phone or deck of playing cards or anything with a flat surface that can rest on the wood block with

a mass ~200 grams. • Digital scale

Make the Friction Block: The wood block in your lab kit will be one of two varieties, a cube or a rectangle. You will need to cut a piece of felt to stick to your wood block on a side that is not the eyebolt side or directly opposite of the eyebolt. If you have a cube shaped piece of wood then the piece of felt that you stick to the block will be a square (~ 5 cm on a side). If you have a rectangular block of wood, use the bigger rectangular side with dimensions of ~13 cm by ~8 cm. Task, Part A (static friction): 1. Record the mass of the wood block, washers and cell phone (or other object with a flat surface if you are not using a cell phone) in Table 1 or a piece of scratch paper. 2. Place the friction block on a table with felt side down and place the bag of washers on top. Hook the spring scale through the eyebolt in a way that you can see the tick marks on the spring scale. Now, using the spring scale, pull on the block with slowly increasing force until the instant before the block starts to slide. Watch the value on the scale to find the maximum value of the force, which should be immediately before the block begins to move. Record the force value from the spring scale in Table 1 (or a piece of scratch paper) so that you can type in this value for the lab exercise later. Record the units for these measurements in the brackets (if you are using Table 1) so that you do not forget them when you do the lab exercise. Repeat this measurement five more times and record spring scale values. This will give you six total data points.

Note: the spring scale is divided into increments of 0.05 increments. You will find that when you take data the scale may be a little past or behind a tick mark. Do your best to estimate the value to the nearest 0.01 N. For example: if you pull on the scale and it is a smidge past 0.45 N, then a reasonable ‘eyeball’ measurement would be 0.47 ± 0.025 N.

It is okay if you get slightly different values for each pull on the spring scale, statistics will be used to take care of this. The professors working on this lab did this experiment and they couldn’t get the exact same value six times in a row! Repeated values of spring scale measurements down to 0.01 N, will look suspiciously like fabricated data and will not be good for a lab exercise score. 3. Repeat step 2 with the felt side of the friction block on the table and with the cell phone (or other object) and bag of washers on top of the block. 4. Repeat step 2 with the wood side (opposite of the felt side) of the friction block on the table with washers on top. 5. Repeat step 2 with the wood side (opposite of the felt side) of the friction block on the table with cell phone (or other object) plus washers on top.

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Table 1

Felt side down Washers on block

[ ]

Felt side down Washers and cell phone on block

[ ]

Bare wood side down

Washers on block [ ]

Bare wood side down Washers and cell phone on block

[ ]

F1

F2

F3

F4

F5

F6

Friction block mass Washer mass Cell phone mass

6. The normal force (FN) has a value equal to the weight of the block, or block and rocks (weight = mass × g). Use FN with the forces in Table 4.1 to find the values for the coefficient of static friction and record your calculations in Table 2 (or a piece of scratch paper). Note: FN is measured in Newtons which can be described as a kg*m/s2, be careful of your units. Table 2

Felt side down Washers on block

[ ]

Felt side down Washers and cell phone on block

[ ]

Bare wood side down

Washers on block [ ]

Bare wood side down Washers and cell phone on block

[ ]

µ1

µ2

µ3

µ4

µ5

µ6

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Task, Part B (kinetic friction): 7. When the block is moving, the frictional force is kinetic. If the block moves at constant velocity, the acceleration is zero and so the net force is zero. (Think about why this is important.) The idea now is to get the block to sustain approximately constant velocity motion. We’ll examine the same four cases we did for static friction, except now you’ll make sure the block moves slowly and steadily along the table as you pull with the spring scale. You do not have to pull the friction block very far to get good data. Pulling the friction block a distance of two block lengths at a constant velocity should suffice. You will notice the force values on the spring scale may vary, and instead of repeating each trial six times, just do one for each surface type. Enter these in Table 3. Do your best to see the high and low value for the force as you pull the block along as steadily as possible. These values should be pretty close to each other. Table 3

Felt side down Washers on block

[ ]

Felt side down Washers and cell phone on block

[ ]

Bare wood side down

Washers on block [ ]

Bare wood side down Washers and cell phone on block

[ ] Flow Fhigh

8. Use the values in Table 3 to find the corresponding coefficients of kinetic friction, and record these in Table 4 (or a piece of scratch paper). 9. We will use a simple approximation, sµ, to the standard error of the mean to find our uncertainty in µ. Find the difference between high and low values and divide by two to estimate the uncertainty and enter that into Table 4 (or a piece of scratch paper). This approximation works pretty well when you have two data points. Table 4

Felt side down Washers on block

[ ]

Felt side down Washers and cell phone on block

[ ]

Bare wood side down

Washers on block [ ]

Bare wood side down Washers and cell phone on block

[ ]

µlow

µhigh

µavg