Lab 7 - March 18, 2015 - Modeling Friction Forces

Lab 7:

March 18, 2015

Brandon Elder

Modeling Friction Forces

Purpose: This lab is split into five parts. The purpose of the first two parts is to use a system of masses, string, wooden blocks, force sensor, and a pulley to determine the coefficients of static and kinetic friction. The purpose of the third and forth part of the lab is to measure the angle at which a block slides down a ramp and measure a mass of a block and use this information to determine the coefficients of friction, some static and some kinematic. The last part's purpose is to use one of the coefficients of kinetic friction we determined to then predict the acceleration of a two-mass system.

Part 1: Measuring Static Friction

Set up the apparatus to look like Fig. 1. Measure the block before you begin. We measured a mass of 131 grams. 

Fig. 1 The apparatus includes a wooden block, with felt, connected by a string to a cup with
water. The cup was filled with water slowly until the block began to move. The amount of water
that was added to the cup is the amount of force that was required to make the system move.

The following steps were taken for the rest of the process.

• Gradually fill the foam cup, the one suspended in the system, with water until the block(s) resting on the table, begin moving. This point represents the value for the max. static friction. Stop adding water the very instant that the block begins to move. 
• Weigh the mass of the cup, with the water still in it. 
• Stack another block on top of the block which is tied to End A of the string. 
• Repeat all previous steps. 

We repeated the experiment, adding one block to the system with each repeat until we had four blocks stacked. The data that we recorded is below, in Fig. 2. The free body diagram of the system is shown below in Fig. 2 as well.

Fig. 2 The recorded values of our block weights and the cup weight when filled with enough water to make the system move. This experiment was performed four times.

Even though we used LoggerPro to determine the coefficient of static friction, we also performed all calculations in order to double check (See Fig 2a and 2b).

Fig. 2a Calculations for the coefficient of static friction. The free body diagram and sum
of forces equations are all drawn on this paper.

Fig 2b The remaining calculations for the 3rd and 4th block trials. The average coefficient
was determined here as well.

Fig. 3 Data inputted into LoggerPro.

In order to graph this data to determine the coefficient of the maximum static friction, we needed to input this data into LoggerPro (See Fig. 3). The slope of the graph of the friction force and the normal force data gives up our coefficient of static friction. In this case, our coefficient of static friction was .305 (See Fig. 4).

Fig. 4 Slope of the line on the graph determines our coefficient of friction static in this experiment.

Part 2: Kinetic Friction

Fig. 5 Force sensor attached to wooden block and pulling it
 across the table at a constant velocity.

Next, we determined the coefficient of kinetic friction. We accomplished this by attaching a force sensor to a string to a block. We then pulled the block across a table at a constant velocity (no acceleration). (See Fig. 5). LoggerPro measure the force that was required to pull the block across the table. Fig. 6 shows the data inputted into LoggerPro and the graphs of the data. From this graph we can determine the average force required to pull each block across the table at a constant speed. We then took that data and made a new data table and graphed the data. From that table, (See Fig. 6a) we were able to look at the slope of the best fit line, which is the coefficient of the kinetic energy.

Fig. 6 These four graphs represent the four trials performed with the four blocks with the force sensor. 

Fig. 6 These four graphs represent the four trials performed with the four blocks with the force sensor. 

Fig. 6a All four pulls are graphed here and the slope of the line is the coefficient of friction - kinetic.

Part 3: Static Friction from a Sloped Surface.

The purpose of this part is to measure the coefficient of static friction, once again. Except this time, we will be using an inclined ramp to track the block. The process is simple. We placed a block with a felt bottom on a board and slowly raised the board until the block started to slide down. Once the block slid down we measured the angle at which the board was at (See Fig. 7 and 8).

Fig. 7 The angle is being measured of the ramp. The block slid down the ramp at this angle.

Fig. 8 The block sliding down the ramp.

The angle at which the block begins to slide is the angle we will use for theta in our sum of forces calculations. Start by drawing out a free body diagram of the set up. The sum of forces in the x-direction (parallel to the ramp) are going to be mg(sin(theta)) = the static friction, because we are looking for the amount of f(static) there is no acceleration to take into account for.  The angle we measured was 19.8 degrees and the mass of the block was 122 grams. With these two pieces of information we were able to perform the calculations (See Fig. 9) and determine the coefficient of static friction to be 0.36. Funny thing is that the coefficient ended up being just the tangent of theta... LOL

Fig. 9 The sum of forces calculations and free body diagram used to determine the coefficient of static friction.

Part 4: Kinetic Friction from Sliding a Block Down an Incline

The purpose of this portion of the lab is to determine the coefficient of kinetic friction of the block as it slides. Because we know that it takes more force to get something to move than to keep it in motion, we are expecting that this coefficient of kinetic friction will be less that what we discovered in part 3 above. The way we will determine the friction is by using a motion detector to track the acceleration of the block as it slides down. We will also record the angle at which the ramp is placed while the block slides down. Once we have those two pieces of information we can set up our free body diagrams and our sum of forces equations (See Fig. 10). The coefficient of kinetic friction for this experiment was 0.337, which is in line with our assumption from above. The kinetic friction force is less than the static friction force.

Fig. 10 The free body diagrams and the sum of forces equations and calculations.

Part 5: Predicting the Acceleration of a Two-Mass System

In this final part of the lab we will take the coefficient of kinetic friction from above, .337, and use it to determine an equation for the acceleration of a block being pulled across a table in a two-mass system exactly like the set-up of part 1 (See Fig. 1). The mass hanging from the string must be big enough to move the system (because we are using the kinetic friction). We will then measure the acceleration in LoggerPro and compare the measured acceleration to our calculated acceleration. The diagrams, formulas, and calculations are below (See Fig. 11). We determined the acceleration on the system to be -.087 m/s2. When we plugged in the motion detector to LoggerPro to measure the acceleration of the block as it slid across the table, the value for acceleration that we received was 0.9458, which is very close.

Fig. 11 The formulas used and diagrams used to estimate what the acceleration on the system would be. 

Conclusion:

We started by using the block-water pulley system to find the coefficient of static friction between the block and the table and graphing the force of static friction with the normal force of the block to find a relationship. The relationship was the coefficient of static friction.

Then we used the force sensor to calculate the kinetic friction of the experiment using the force graph of the recorded data. After that we found the coefficient of static friction of the wooden block on top of an inclined ramp. Next, we used the acceleration found from the block sliding down a steep ramp with the motion sensor to calculate the coefficient of static friction for the ramp. Finally we predicted the acceleration of the system by using the previous coefficient of static friction.