16- Sept. - 2014 Friction Lab

Friction Lab

Objective: 
 Use the lab set ups to find both  s  and k  between wooden block(s) and the surface it is on.

Set- up (4 of them):

1) We used 4 wooden blocks (one is piled on top of the previous per trial with the first having a specific red fabric underneath), around 1 m of string, 2 cups with on filled with water, weights, dropper, and a pulley as seen in (fig 1a). We used this set up to find the static friction of the block by comparing its total mass to how much water it takes to make the block move.

Figure 1a. The set up with the initial block with a pulley and string with a
 cup with water at the end of it 

2) We attached a force meter to the same initial block and attempted to drag it at a constant speed. Each trial is the number of blocks stacked on top (up to 4).

3) We set up a sloped new surface and tracked the acceleration of the block sliding down with a motion detector set up parallel to the surface as seen is in (fig 3).

4) We attached a pulley to the top of the sloped surface and attached 500g to the end of the string so its weight will overcome the static friction. We set up the block with a motion detector and one end of the ramp to track its acceleration as seen in (fig 5).

Part 1)
 Using the first set up we measure the following spreadsheet as the results of each trial where the Normal Force was the weight of the stack of blocks for each trial and the force of Max Static Friction was the weight of the cup and water that resulted movement from the block.

Figure 1b. The spreadsheet from excel of the different values and measurements we found

Figure 1c. The graph of the Max static force vs. Normal force where the slope is the s

From the graph above, we found our slope (s) to be .3546. 

Part 2)
 For this part of the lab we used the second set up by using the force sensor and pulled at a constant speed to record the average force of kinetic friction after analyzing the data seen in (fig 2a.)

Figure 2a. a graph with all 4 results for the force 
readings and we found a statistical average (mean)
to find our average kinetic friction coefficient k 

Using the known mass for each trial and our calculated values of Normal Force and the Average Kinetic Friction (from the figure 2a), we graphed the Average Kinetic Friction vs. Normal Force and linear fitted it.

Figure 2b. Similar to the spreadsheet in part 1, we use excel to graph the values of Average kinetic friction along the axis of Normal Force.

Figure 2c. The resulting graph with a linear fit where we found our slope (k) to be .2914 and seeing that it is smaller than our value for the coefficient of static friction is reassuring that it may be accurate.

When we used linear fit, we got the slope (k) to be .2914.

Part 3)
 Using a new block with a mass of .273 kg, we then used the third set up and slowly tilted our aluminum flat- track until the block started to slide due to gravity overcoming its static friction.

Figure 3. Our third set up for the lab where 
we have a sloped surface and motion detector 
to track its position and calculate acceleration 
when we change its angle.

We found that the angle in which the block starts to slide is approximately when theta is .2443 rads above the horizontal. As seen in (fig 6.) We derived an equation and solved:

s= tan(theta)

s= tan(.2443) = .2493

Part 4)

 From the last set up we used the same block and flat track. However, we made the track go from .2443 rads to .4363 rads. Using the motion detector (also seen in fig 3.), we recorded its velocity and velocity changes to find the acceleration of the system. To do so, we had to make a linear fit for the graph and read its slope.

Figure 4. Our resulting graph from the part 3 set up where
our average slope in the linear fit is m= .8548

After reading its slope for average acceleration to be 0.8548 m/(s^2), we used it in (fig. 6) to find the system coefficient of kinetic friction which came to be a very interesting value of k= .370. At first it was a surprise that the coefficient was higher than our previously found static coefficient, but then we realized that this was a different angle so there are different coefficients. To check, we calculated s= .4663 in this case. With that reassurance, we moved on to part 5.

Part 5)

Figure 5. Our final set up with a pulley and weight to
 drag the block along a slanted surface.

Before we performed this lab, we had to predict the system's acceleration in which we derived the following:

asys= g(mwt -mbl (sin(theta) + cos(theta)k) 

(mbl + mwt)

Theoretical value:

asys= 2.810 m/(s^2)

For this lab, we used the fifth set up and hung a mass of .4 kg and recorded the results.Unfortunately our actual graph was lost, however we have recorded the actual acceleration in this scenario as aact = 2.695 m/(s^2) up the ramp. Comparing the two values shows that there was a small amount of error:

atheo= 2.810 m/(s^2)

aact= 2.695 m/(s^2)

approximately -4% than theoretical

Figure 6. Lab notes and work for parts 3 to 5 showing derivation of equations and our calculations