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.