Lab 7 Modeling Friction Forces

Purpose: The purpose of the laboratory is to examine the relationship between static and kinetic friction forces.

The equipment we used in this experiment were a scale, pulley, Styrofoam cup, string, track, and 4 wooden blocks.

In this experiment we had five different scenarios in which we took data for using the data collected from each we drew body diagrams to get our net force formulas and used those equations to find the coefficients for kinetic and static friction and then we used logger pro and collected data for kinetic friction and compared what we got from the computer with the kinetic friction that we solved for from our equations.

For the first scenario we are going to measure the mass of the block being pulled then we are going to add water to the cup until there is enough water in the cup to make the block move. Then we measured the mass of the cup with the amount of water that made the block move.

We continued this process always adding another block for each trial until we had four blocks total.

We gathered the data for the mass of the water that made the block move which is represented by C. and the mass of the blocks represented by B.

Using our data we made a graph of friction and time and the slope of our graph was our coefficient for static friction which turned out to be .2912.

For the second scenario we used a force sensor to examine kinetic friction. First we calibrated the force sensor, then we measure the mass of the block we were going to pull. We tied the string to the force sensor and pulled the block. logger pro recorded the force of the pull in newtons for each trial and we recorded the data on the white board.

 

The mean values that we got for friction came from the data collected by logger pro in the bottom photo .

 

We used the data for Normal Force and Friction to create a graph and the slope of our graph was the coefficient of kinetic friction.

 
Next placed one block on a horizontal track and then we raised the track until the block slide down the track and at that point we measured the angle that it took to move the block. Using the measured angle and the measured mass of the block we used free body diagrams to get our net force formulas to calculate the coefficient of static friction

  For the fourth scenario we set up the system so that the track is at an incline steep enough so that the block will accelerate down the track. We measured the angle of the incline of the track. And we attached a motion sensor at the top of the track so that we could measure the acceleration of the block as it went down the track. Using the data for the acceleration and the angle measured we are able to calculate the coefficient of kinetic friction using the formulas derived from the free body diagrams as we did in the bottom pic.

For scenario five we had a two mass system on a track and we using the coefficient of kinetic friction we had to derive an expression to find the acceleration of the block on the track using a large enough mass to accelerate the system. The mass that we used to accelerate the system was .05 kg . Using the mass and the static friction from scenario four we were able to find the acceleration of the block.

Next, we used a motion sensor and logger pro to measure the actual acceleration of the block using the same hanging mass and compared the acceleration we got from logger pro with the acceleration that we got from the calculation. As you can see from the bottom photo the slope of the graph is the acceleration which turned out to be .4564 while our calculated acceleration turned out to be .459 m/s^2 . Our results were pretty close to each other but not perfectly the same because there many factors that could have lead to some error.

 

In conclusion, we learned out to calculate the static friction and kinetic friction coefficients depending on what we were given. we also saw how static friction is greater than kinetic friction. And we were to calculate acceleration of a system and compare it to the acceleration we recorded form logger pro.

Propagated uncertainty in measurements

Purpose: To learn how to calculate the propagated error in each density measurement to find out whether or not your measurements are within the experimental uncertainty of the accepted values.

The vernier caliper will be used to measure the height and diameter of the metal cylinders.

The scale will be used to measure the mass of the metal cylinders.

After we have collected the measurements of mass height and diameter of the metal cylinders. we are going to use the formula for density to calculate the propagated error in our measurements. Then we will calculate the density from our measurements and add the propagated uncertainty to see if our measurement for density is within the experimental uncertainty of the accepted values for the metal cylinders that are copper zinc and Iron.

 

 

 
Using these measurements we found out the propagated error for the density by adding the uncertainty in the mass with the uncertainty in diameter and the uncertainty in height. To find out the uncertainty in the mass we took the partial derivative of the mass in the density formula and pretended all the other variables were constants. After finding the partial derivative we multiplied the partial derivative with the accuracy of the instrument we used which was the scale, so we multiplied the partial derivative by .1. After getting the uncertainty of each measurement we add them all up to get the uncertainty for the density. Then we found the density of the metal using the density formula and added or subtracted the uncertainty for the density and the accepted value for the density should fall within the range of our density and uncertainty which in our case it did. Our uncertainty and density for the copper cylinder was 8.182 +or- .75089 g/cm^3 and the accepted value is 8.83 g/cm^3. for our zinc cylinder we got 6.60169 +or- .62572 g/cm^3 and the accepted value is 7.140 g/cm^3. The only density that didn't make sense was our iron we got 6.36379 +or- .5996 g/cm^3 which is not within the range of the accepted value 7.874 g/cm^3.

 After we learned how to calculate propagated error we did the second part of the experiment which involved calculating the mass of a hanging object held up by two strings we did this for two systems.

The first thing we did was take the measurement of the angles of the strings and the force of the tension on each string .















Next, we drew free body diagrams to find our the equations of the net force and solved to find the unknown mass for each system.

After we found the mass of each object we had to find the propagated error to account for the error in our instruments.

 

So we learned how to calculated propagated error to show that our values are within the accepted values and we applied what we learned in the second part by finding the propagated error of the unknown mass.

Free Fall Lab determination of g

Purpose: the purpose of this lab is to show whether or not an object at free fall will accelerate to the ground at 9.8 m/s^2 due to gravity and in the absence of all other external forces.




This apparatus is used to mark the position of the free falling body during the same intervals. A spark generator marks the position on a spark sensitive tape giving a record of the fall.

To fulfill the purpose of the lab we are using the data we collected and putting it in an excel worksheet. In the excel worksheet there will be 5 columns of data imputed into the spreadsheet. The first column is the Time column at every 1/60 of a second. The second column is a Distance column in this column we chose a dot to be the t=0 and we measured the distance between the dot and the following dot and kept doing so until we felt like we had enough data points. The third column represents the change in position between the dots. The fourth column we calculated the mid interval time. Finally in the Fifth equation we calculated the mid interval speed.

 

 

 

 

 

 

Using the information from the excel columns D and E we created a scatter plot of velocity and time. The x- axis represents the time and the y-axis represents the velocity. This graph is linear showing that the acceleration of the object is constant and not increasing or decreasing.

 

 

 

 

For the following graph we used columns A and B from the excel data to create a scatter plot for position and time. Position being the y-axis and time being the x-axis. For this graph we had to add a trendline with a polynomial fit because a linear trendline would indicate that the velocity is constant but because the velocity is increasing the graph is not a straight line.

 

 

In the end we can use either graph to find out the acceleration due to gravity keep in mind there is going to be error so the exact value you will get might not be 9.8 m/s^2

 

 

Questions / Analysis:

 

1. To get the acceleration due to gravity from the velocity/time graph we just take the derivative of the equation of our graph y = 950.53x + 50.658 which becomes a = 950.53 which is in centimeters so converted to meters it is 9.5053 m/s^2 and the accepted value is 9.8 m/s^2 which is pretty close considering the equipment we used is not the best and there are other factors that could have caused error.
2. To get the acceleration due to gravity from the position/ time graph we just take the second derivative of the equation y = 472.88x^2 + 50.937x + .0373. The second derivative gives the acceleration to be a = 945.76. This ends up being 9.4576 m/s^2 which is also a good value compared to the accepted value of 9.8 m/s^2





23-Feb-2015 Deriving a power law for an inertial pedulum

Purpose: The purpose of the laboratory is to find an equation that relates mass and period and can be used to determine values of unknown masses .

inertial balance was used to measure the inertial mass by comparing objects' resistances to changes in their motion.

 

data taken from the experiment was plotted on logger pro.

 Different mass values for Mtray were used to until the linear fit gave a correlation coefficient very close to 1. The range that gave us the best lines for the graph was when the mass of the Mtray was between 280 and 300.

In the lab we were able to come up with an equation that gave a really good close approximation to our unknown masses the values that we plugged into the equation for the slope and y-intercept came from logger pro when we plugged in the smaller value and larger value for the mass of the Mtray.
The calculations show that we were able to get the calculated mass to be pretty close the actual mass of the first unknown mass was 369 grams, but when we calculated the mass we got 370.45 grams. While for the second unknown mass the mass we received was 148 grams, and the calculated mass was 144.76 grams.

there is some error that could have occurred because of many factors for example the mass of the weights placed on the inertial balance were never weighed before we just assumed they were the masses they read.