Lab 7: Modeling friction forces

Purpose: The purpose of this lab is to find a model for kinetic and static friction.

This lab was separated into five different parts.

The first part of this lab was to find static friction of a block that was  hooked on to a hanging cup which we slowly filled with water until the block started to move.

W measured the mass of the blocks on a scale and recorded it on to our data table.

   This is a picture of the the first part of the lab. As you can see a mass of blocks is attached to ta hanging mass via an ideal pulley. Static friction allows the blocks to remain at rest.

Part 2: kinetic friction

For this part of the lab we used a force sensor to to calculate kinetic friction of a moving object.

First we had to connect our force sensor to logger pro. we calibrated the sensor by using a 500 grams hanging mass. The picture above shows how this step was executed.

After the force sensor was calibrated we used it to drag a wooden block along the table for around 4-5 seconds.

This is a picture of the block being pulled with a constant force.

While we pulled the sensor, logger pro was recording the entire motion of the block.

Our graph shows four different lines because the experiment was ran four times each time with different blocks. We had to store and analyze each run in order to get the average force exerted.

After we recorded our four forces we created a graph of Normal force v.s. Force, this graph gave us our coefficient of kinetic friction.

Here is a closer look at our N v.s. F graph.

Part four:Kinetic friction from a sliding block.

 Set up: we used an incline, a motion sensor and logger pro. We placed the block on top of the incline about five inches away from the motion sensor. We let go of the block and calculated its acceleration with logger pro.

I

This is our velocity graph. We got the acceleration of the block by calculating the slope of the v v.s time graph.









Part 5: Calculate the theoretical acceleration of the block by using the coefficient of friction from part four.

lab 6 propagated uncertainty in measuremensts

Purpose: to find density of different cylinders along with the propagated error.

At the beginning of class we received three cylinders which were made up of copper steel and aluminum. We were instructed to solve for the density of the volume. 

The Picture above shows the three cylinders (steel,copper and aluminum). Along with the cylinders there is a vernier caliper (that fancy tool at the bottom)which is a tool that we used to measure the height and diameter of the cylinders.

Here is a picture showing how we measured the height.

A scale was used to get the mass of all three objects. 

The picture below  shows the measurements of all three objects.

We took the data from the table above and solved for the density of copper steel and aluminum.

After we solved for the density we had to solve for the propagated error of our calculated density.

We solved for density of all cylinders by using the the equation D=M/V M=mass,V=volume.

Which turned out to be D= M/Pi*(r^2)*h.

We also had to solve for propagated error of density by taking partial derivatives of the radius, height and mass.

The equation came out to be following dd= (1/Pi*(r^2)*h)*DeltaM + (M/Pi*(2r)*h)*DeltaR + (M/Pi*(r^2)*1)*DeltaH.

For Part two of the lab we had to figure out the mass of the hanging object.

Here is a picture of the initial hanging mass.

As you are able to visualize there is a newton measuring device attached to each side of the hanging mass.

The one to the left read 5 N + or - .25 N and the one to the right read 6.75 N + or - .25 N.

After we recorded the newton readings we had to measure the angle of the strings with this clever device on the left.

Here is a picture of when we measured the angle.

Here is another picture of the lab set up.

After we had all of our data we set up an equation to find the mass of the hanging object by taking the components of Y of both the strings. The equations came out to be Mass= (F1sin26+F2sin40)/g, g is the acceleration due to gravity.

F1 = 5 N +or- .25 N @ 26 degrees  +or- 2

F2 = 6.75 +or- .25 N @ 40 degrees  +or- 2

We derived our propagated error at the bottom, by taking partial derivatives of the forces

 and angles of the angles and forces we measured. Since calculus does not recognize degrees we had to switch our degrees to radians.

We repeated the previous steps for other hanging masses and turned them in at the end of class.

lab 4 Air resistance

Purpose: The purpose of this lab is to determine the relationship between air resistance force and speed.

Formula: F(air Resistance)=kv^n

Tools: we used logger-pro to record the coffee filters falling from the second floor of the tecnology building. 

To the left we have different  group members releasing the coffee filters off of the second floor.

While the filters were falling other group members recorded their motion using logger pro. 

This is a picture of group members recording the motion of the filters.

Note: Five different trials were done, groups started with one filter and ended with five.

Back at the lab we created a position vs. time graph. We did a linear fit on the position vs time  graph to get the slope , the slope of the graph represents the final velocity of the coffee filters.

Trial 1: 1 coffee filter- terminal velocity= -.8164 m/s

Trial 2: Two coffee filters Terminal velocity= -1.216 m/s

Trial 3: 3 Filters Terminal velocity= -1.650 m/s

Trial 4: 4 filters Terminal velocity=-1.865 m/s

                                          After we found our velocities we created a force vs. velocity graph to get our values of K and n.



Spread sheet is to the left.

To the right we have the proportional fit Force vs. Velocity graph.

K= .01279

n= 2.042

F(air resistance)= .01279 v^2.042

Lab 3 Non-constant acceleation

Purpose: To find out how far an elephant travels while it decelerates with help of a rocket.

Question: A 5000-kg elephant on  friction-less skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. Once on level ground a rocket attached to the elephant turns on generating a 8000 n thrust in the opposite direction of the elephants travel.

The left of the picture shows the body as it travels down the hill with the rocket off.






The right side of the picture shows the elephant with the rocket already activated. The rocket loses weight at a rate of 20 kg/s.

We solved this problem Mathematically and numerically.

Mathematically:






With the given information we were able to find Acceleration as a function of time by manipulating F=Ma into a(t)=F/M. The actual equation is shown on the left.












In order to find Position as a function of time we had to integrate a(t). Luckily professor Wolf was nice enough to integrate the problem for us.



The equation to the left is the position as a function of time after it was integrated by professor Wolf.















W found out that it takes the elephant traveled for 19.69075 seconds before stopping.
We plug in the time into the equation above and we found out that the elephant traveled 248.7 meters before coming to a stop.

Numerically:

Another approach we took to solve the problem was a numerically approach by using excel.
We plugged in our numbers into excel and we let it solve it numerically.






These are two copies of our excel files.

t= time
a= acceleration
Delta V= Change in velocity
V= Velocity
V_ave= Average velocity

                                          Delta-x= Change in X

                           X= Position 

The copy to the left shows a velocity of 0 m/s at t= 19.69, The position at this time is
 248.698165 m.






In conclusion our analytically and numerically answers both match.

lab 2 Free fall lab

Purpose: The purpose of this lab is to examine the validity of the statement: In the absence of all other external forces except gravity, a falling body will accelerate at 9.8 M/s^2.

  Free fall apparatus


This apparatus measures the speed at which an object falls.  A body with mass (m) is held  at the top by an electromagnet. When the body is dropped a spark generator records dots on a strip of paper every 1/60th of a second.














Although we were unable to use the free fall apparatus we did receive a strip of paper that contained dots created the apparatus.


This is the strip of paper we received, it contains light dots that were imprinted by the spark generator on the free fall apparatus. Each dot is exactly 1/60th of a second apart from each other. we took the strip and measured the distance from from the dots. After we recorded the distance we created an excel file.



These are the points we measured along with time, change in distance and velocity after we put them
on a excel file. To the right of the file we have our velocity vs time graph which shows velocity increasing as time increases.

Question analysis:
        We are able to get our acceleration from our graph by performing a linear fit to the graph with gives us the slope of the graph, the slope of the graph is the acceleration due to gravity.
   
      Once again we are able to get our acceleration from pour position vs. time graph by performing a linear fit to get the slope. The slope of the graph is the acceleration due to gravity.

    Our Acceleration due to gravity
y came out to be 940 cm/s^2 of 9.40 m/s^2.
To find out how off we were we take the Absolute value of Accepted- Actual, our value was .41 m/s^2 off from the original value.

     A possible reason for the error is that our drop was not long enough. We might also need more sophisticated equipment to get a closer reading

Part 2:
Errors and uncertainty.
After we derived a measurement for gravity we had to analyze the data from the entire class by combining the results of the 9 groups in the class on an excel spread sheet.

Here is a copy of our excel sheet, at the top right we have the actual value for gravity followed by the calculated values from our class and ending with the average of all ten.

After we found our average, we had to add a new row and find the deviation from mean by subtracting the class calculated values from the average one by one as shown in rows B2-B12.

 After we found our deviation from the mean we squared then all to find our standard deviation.








The pattern in the our calculated g's is that they are all close to the value of gravity, none of the values are way off.
The average of the values allows us to take one set value for the entire class to compare to our separate values to find our standard deviation.
    One thing that might account for the difference in our value from the other values is that we have different techniques for rounding, which accounts for a systematic error.

The part of this lab is for us to learn how to calculate how incorrect our answer is from the original value. We learned that in order to get a standard deviation we have to have all of our numbers positive. We can get all of our number to be positive by either placing absolute values around the subtraction from our calculated and original value. Another way to make all of our values positive square then all and the the square root them after.