24 September 2014: Circular Motion and the Relationship Between Angular Speed and the Angle of a String

Purpose: To derive a relationship between angular speed (ω) and the angle of a string (θ) for a particular apparatus. 


The apparatus below rotates about a fixed point at some speed with the

22 September 2014: Centripetal Acceleration as a Function of Angular Speed

Purpose: To find centripetal acceleration as a function of the angular speed of the system.

15 September 2014: Coefficients of Friction

Purpose: To find the coefficients of kinetic and static friction on a horizontal and an angled surface.  

     To predict acceleration of a two mass system with one mass on a slope.

8 September 2014: Propagated Uncertainty

Purpose: Part 1: To calculate the propagated error in each of one's density measurements. Determine

     whether or not those measurements are within the experimental uncertainty of the accepted values.

     Part 2: Determination of a suspended unknown mass.


     The apparatuses below are a scale accurate to 0.1 grams and a caliper accurate to 0.01 cm.

     We used this equipment to measure the mass, the diameter, and the height of the three cylinders of 

brass, steel and copper. 

Below is partial calculations of density and its propagated error

The density of brass is 8.43g/cm^3 with p +/- dp 

Part II: Determination of an unknown suspended mass

     

      A labeled picture of the unknown suspended mss

Th

10 September 2014: Projectile Motion Lab

Purpose: To use one's understanding of projectile motion to predict the impact point of a ball on an

     inclined board.

Equipment:
     1. Aluminum "v-channels"
     2. Steel ball
     3. Board
     4. Ring stand
     5. Clamp
     6. Paper
     7. Carbon paper

     The apparatus was used to release the steel ball from a point on the sloped aluminum "v-channel"

so that it rolled down the first v-channel onto the second one, which ended at one of the edges of the

table, so that the ball would leave the table at some velocity and drop some distance away from the

edge of the table. The carbon paper along with the another piece of paper would be positioned so that

when the ball hit the floor it would hit the carbon paper, thus leaving a mark on the other piece of

paper, at the point of impact.

     We measured the height of the end of the horizontal track to be 88.5 cm. After dropping the ball 

the displacement from the edge of the table on the floor in the x direction found to be 59 cm after a 

series of five tests.

      From this we were able to calculate launch velocity by finding t in the equation h=-(1/2)*gt^2 as 

we know the height we found that t=0.425 seconds. With t and the known displacement we were able 

to find v in the equation ∆x=vt finding the velocity to be 1.388 m/s. 

     

     With this new information we were able to derive an equation that would allow us to determine 

how far the ball would strike a plank on an incline of some angle Lcosθ=vt. From this we find t to be 

t=Lcosθ/v. With the equation for height we find that h=1/2gt^2, which becomes Lsinθ=(1/2)gt^2. We 

then replace t with the equation for t that we found earlier Lsinθ=(1/2)g(Lcosθ/v)^2.     

     After placing the board down we found the angle between the board and the ground to be 51°. We 

then input this along with the other information that we know into the formula found above. 

Lsin(51)=(1/2)*9.8*(Lcos(51)/1.388)^2. Doing the math the prediction for L comes out to be 0.452m.  

Our setup with the plank of wood

     The experimental distance turned out to be d±σ = 0.460m this has a 1.8% error from the 

theoretical distance. Sources of error or uncertainty may come from an incorrect measurement of 

the plank or a different releasing height of the ball.

Summary

     We setup an apparatus that allowed us to test projectile motion. Comparing our theoretical value

based off the physics equations to the experimental value that we measured as a result of our

experiment. Finally, commenting on possible sources of error or uncertainty.

8 September 2014 Modeling Air Resistance

Purpose: Part 1: To determine the relationship between air resistance force and speed.
                Part 2: Model the fall of an object including air resistance.

Equipment used:
     1. 15 Coffee filters of the same size: to drop and measure air resistance
     2. A 2 meter stick
     3. A Macbook Pro with Logger Pro, Video Capture, and Microsoft Excel: To map and chart the
     data

     The two pictures below show two of five separate tests where we as a class, in our groups, in

dropped five sets of coffee filters from a balcony. The the sets consisted of 1, 2, 3, 4, and 5 coffee

filters respectively. Using video capture on the Macbook Pro we were able to record the fall of the

coffee filter(s). With Logger Pro we were able to map out the rate and acceleration at which the

coffee filter(s) fell. The dots represents the approximate location of the coffee filter(s) at some time.

The 2 meter stick was used to scale our distance during the fall of the coffee filter(s).

Pictures of Video Capture Analysis

     Below are the five position over time graphs that we found and their respective slopes.

     Above is our mg vs velocity graph as the set of 5 coffee filters worked best we shall use this below 

to compare our experimental data against our theoretical data. The slope becomes our k that is 

     While we were gathering our equipment for the lab we found that the coffee filters that we used 

were each roughly gram making mg=0.01 N. Using the slopes of ends of the position over time 

graphs we had the terminal velocity. 

   

  The sum of all forces for this lab was ∑F=ma=mg-R this give us an acceleration of a=(mg-R)/m. 

R is the force of air resistance. Using the model R=k*v^n where k is some constant and n is some 

power we were able to insert it into our formula for acceleration a=g-k(v^n)/m. When the

acceleration is 0 k becomes 0=9.8-k((2.771)/0.005) k comes

3 September 2014: Non-Constant Acceleration

Purpose: To solve a problem with a non constant acceleration

For this we used only Microsoft Excel 

      As a class, along with the Professor Wolf, we solved this problem. Following the steps on the

handout and those told to us by the professor.


      Based off the original instructions my group and I found the time, acceleration, the average

acceleration, the change in velocity, the velocity and the distance for the elephant. The first 35 points

are shown below when the interval of time is 0.1 seconds. Thanks to Excel the numbers and

calculations were easy to numerically integrate.

      Below is when the elephant's v=0 at some time in between 19.1 and 19.2 seconds in that time 

the elephant traveled about 243.8 meters. The time 19.1 and 19.2 seconds are highlighted.

    

 Here is how the problem is solved analytically. (From top to bottom). 

     

    

     When the time interval is 1s instead of 0.1s where v=0 at some time in between 19 and 20s 

these two times are highlighted creating a higher margin of uncertainty.

     When the time interval is 0.5 seconds instead of 0.1 seconds where v=0m/s at some time between 

19 and 19.5 seconds these two times are highlighted creating a higher margin of uncertainty than 

when the time interval is 0.1 seconds but less than when the time interval is 1 second.

Summary

     We solved a problem containing a non-constant acceleration as a class. Finding how long it would 

take to slow down an elephant on roller skates and how far that elephant went. The time when 

v=0m/s was 19.69 seconds and the distance was about 244 m numerically and I got 248.7 m 

analytically.

Conclusion

     Numerically I miss calculated at some point on the Excel sheet that I was uncertain how to fix as 

the analytically the math is correct. The time interval becomes small enough when there is a change 

of less than 1% as it fits into a three significant figures.