Lab: Ballistic Pendulum

Ballistic Pendulum

Isaiah Hernandez and Tony Wu

Purpose: Determine the firing speed of a ball from a spring-loaded gun. 

Theory/intro:

This experiment is a representation of an inelastic collision where momentum is conserved before and after the collision. In the beginning of this case, there is only momentum in the ball being fired at the cube and the cube is at rest. Afterwards, the ball and the cube act as a single object and the momentum afterwards is the mass of both the ball and the cube multiplied by the final velocity at which the system was moving after the collision. After the collision, the system is gaining potential energy as the height increases but also losing kinetic energy. 

An equation for the final velocity of the system was found using the conservation of energy and it could be substituted in for the same final velocity variable in the equation for conservation of momentum. 

A summary of apparatus/experimental procedure:

Before each trial, we had to align the cannon with the cube so that the ball would make it into the cube. The apparatus was cocked and fire and the resulting angle was recorded.  

A list/table of your measured data:

Analysis:

Lab 9: Centripetal Force with a Motor

Centripetal Force with a Motor

Isaiah Hernandez and Tony Wu

Purpose: Develop a relationship between Ꝋ and ω.

Theory/intro: F=ma

Using the free body-diagram for the mass being swung, an equation for the net force on the system can be derived and set equal to the mass of the object times its acceleration (in this case is centripetal acceleration. Omega can be solved arithmetically in terms of :

theta(angle made with the vertical), R(distance from the center of rotation to the start of the string), and L( the length of the string). 

A summary of apparatus/experimental procedure: 

The motor spins the at a higher angular speed which is cause for an increase in total radius and angle theta. Record the time it takes for the apparatus to complete 10 rotations and the height above the ground for the hanging mass during several trials. 

A list/table of your measured data:

 

A list/table of your calculated result(s)/Graphs of your data:

Correlation of Theoretical v. Experimental Values of Omega for each case 

Explanation of your graph/analysis:

Data Tables: 
Once obtaining the time it took for one revolution, we were able to get the amount of rotations per second. Flip that number and get the period (seconds per a single rotation). We then multiplied the period for each case by 2Π which would give the angular velocity. 

Graph: 
The graph above shows how close our value was to the expected value. It is expected to have a correlation of about 1 but we were off by a bit in our experimental values. 

Conclusions:

As we increased the omega of the system, the radius (from the center of rotation to the mass on the x-axis), the angle from the vertical, and the height of the swinging object all increase proportionally.   

Lab 8: Centripetal Acceleration v Angular Frequency

Centripetal Acceleration v Angular Frequency

Isaiah Hernandez and Tony Wu

Purpose: To determine the relationship between centripetal acceleration and angular speed. 

Theory/intro: Centripetal acceleration is the inward acceleration of object. It is denoted by the formula a_r =  v² / r.     

A summary of apparatus/experimental procedure:

Collect period and acceleration data for a variety of rotational speeds by varying the voltage from the power supply feeding the scooter motor. 

A list/table of your measured data: 

Data table of varying mass, radius, or omega. 

A list/table of your calculated result(s)/Graphs of your data:

This graph showsthe effect of varying the radius of the apparatus.




This graph shows the effect of varying the omega of the apparatus.





This graph shows how the effect of varying the mass of the apparatus.

 Conclusions:

An increase or decrease in one out of the three variables that make up centripetal acceleration  (mass, radius, or omega) led to a proportional increase in the other two variables as analyzed from the formula for centripetal force:  

Lab 5: Trajectories

Trjectories Lab

Isaiah Hernandez, Tony Wu, Leslie Zho

Purpose:
To use projectile motikon concepts to predict the impact point of a ball on an incline board.

Theory:

We will be able to predict the impact point of a ball on an incline board by viewing the motion of the ball in terms of x and y components and using algebra to solve for the distance in terms of the two components.

A summary of apparatus:

Calculated results:


Explanation of your graph/analysis:

Using this formula, our team was able to predict the point of impact of a ball in projectile motion given the angle of incline and initial velocity.

Lab 7: Modeling Friction Forces

Modeling Friction Forces Lab

Isaiah Hernandez, Tony Wu, Leslie Zho

Sept. 12, 2016

Purpose:
Perform a series of experiments to determine the coefficient of static and kinetic friciton of the back side of a white board on a block with a layer of felt. 

Theory/intro:
Static friction is the force acting on an object that opposes the direction of motion in order to keep the object from moving (static: all forces cancel each other out in the x and y planes.)
Fsmax = μs η

Kinectic friciton is the force acting on a moving object that opposes the direction of motion. 
Fk = μk η

A summary of apparatus:

We were required to perform 5 different experiments revolving around the general concept of friciton (Kinetic and Static). We performed 4 trials and recorded corresponding data for each case. Amongst these cases were:
1. Static friction on a flat surface.
2. Kinetic friction on a flat surface.
3. Static friction on an incline.
4. Static friciton on an incline.
5. Kinetic friction acting on a mass-pulley system. 

Table of measured data:


Graph (Weights v. Mass) for Test 1 involving static friciton on a flat surface:



Graph (N v. Fricitonal Force)for Test 1



Graphs of calculated results:


Explanation of graph:
The graph for the calculated results depicts the experimental measurements and results for the coefficient of both kinetic and static friction coming from the board and acting on the block in each of the 5 cases.

Conclusions:
The results from the experiment show that the acceleration of a system is directly affected by the mass of the object being analyzed. As the a mass of the object increases, the acceleration decreases due to the opposite dirction of the friction force on a moving/static object. 

Lab 6: Propagated Uncertainty in Measurements

Propagated Uncertainty in Measurements Lab

Isaiah Hernandez, Tony Wu, Leslie Zho

Purpose: Measure the Density of Metal Cylinders 

Theory: The density of aluminum tin cylinders can be obtianed manually by measuring both the mass and volume of the samples and dividing the mass by the volume.  

A summary of apparatus:
Our team was asked to select two samples and record the diameter of each cylinder in order to calculate its volume and measure each mass separately. After the experimental density value for each cylinder was found, we had to calculate the propagated uncertainty of this value.

Table of calculated results:


Calculations for propagated uncertainty of density :


Conclusions:
Our team was able to find the density of Alminum and Tin using the formula Density = Mass/Volume. After deriving a general equation for density by specifically using the volume of a cylinder we were able to calculate the propagated uncertainty for each density.   

15-Sept.-2016: Non-constant Acceleration

Non-Constant Acceleration Lab

Isaiah Hernandez, Tony Wu, Leslie Zho

Sept. 15, 2016

Purpose: Find how far an elephant on frictionless roller skates travels (with given conditions) before coming to rest. 

Theory: There is a long and tedious analytical approach to solving the problem at hand and this method is shown on the first page of the lab description. We were asked to find the same result by instead entering the data into an excel worksheet.

A summary of apparatus:
A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a 1500-kg rocket mounted on the elephant's back generates a constant 8000 N thrust opposite the elephant's direction of motion. the mass of the rocket changes with time so that the mass with respect to time is equal to 1500 kg - 20 kg/s*t.

A list/table of your measured data:


Explanation of your graph/analysis:
 Based off of the data entered into the excel worksheet, we found that it takes the elephant approxiamtely 2.40 seconds before reaching constant speed with no acceleration. This does not necessarily mean the elephant is at rest. The elephant will continuously travel at a constant speed of about 1.6446 m/s until some outside force opposes its motion.

Conclusions:
The elephant in this problem was found to potentially keep rolling forever even after the rocket on its back stops accelerating it forward. The acceleration kept decreasing as time went on and eventually reached a value of 0 m/s^2 but this only means that the velocity will constantly stay at whatever value it was found to be at the same instance the acceleration went to 0. This is because the elephant is resting on frictionless roller skates. Without an opposing friciton force, the elephant will virtually keep moving forever. 

12-Sept.-2016: Free Fall Lab

Free Fall Lab

Isaiah Hernandez, Tony Wu, Leslie Zho

Sept. 12, 2016

Purpose: 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."

Theory: In "perfect" conditions, any object found in free fall will be accelerating downwards towards the earth's core at a rate of 9.8 m/s^2 due to gravity on Earth. The class was responsible for using the given apparatus and an excel worksheet to represent a correlation between the experiment and the acceleration due to gravity.  

A summary of apparatus/experimental procedure:
 Our team was given a strip of paper tape that was hooked up to a sparker thing and released as the device began to make marks on the tape. We had to measure the distance between each mark and record them into an excel worksheet. 

Table of measured data:

Table of calculated results: 

Explanation of your graph/analysis:
 In the table of measured data, we inserted a graph to represent the relationship between the interval time that passed and speed at which the paper was being zapped. We used a linear fit to obtain the function that best aligned with the plotted data. We found that this graph had a slope of 0.988 m/cm^2 which can be converted to 9.8 m/s^2. This converted value corresponds to the value of acceleration due to gravity (9.8 m/s^2). 

 Conclusions:
The statement presented: "In the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2," was proven to be true during this experment. The apparatus and analyzed data showed that the paper strip fell at a rate of approximately 9.88 m/s^2 which closely matches the value of acceleration due to gravity (9.81 m/s^2). 

06-Sept-2015: Deriving a power law for an inertial pendulum

 Finding a relationship between mass and period for an inertial balance

Isaiah Hernandez, Tony Wu, Leslie Zho

September 6, 2016

       Purpose: The purpose of this experiment is to find a relationship between mass and period for an inertial balance

       Theory: I believe that the more mass added to the inertial balance will lead to an increases in period because objects with higher masses have more of a resistence. 

       Procedure: We first attached the balance to the table using a c-clamp. The device we used to record the data for our experiment was a photogate. The photogate was set up in front of the balance. A LabPro was set up through the class laptop and hooked up to the photogate. We begun experimenting and recording the period of the intertial balance with no weight and had to increase the weight added by incriments of 100 grams until we hit 800 grams. Afterwards, we executed the experiment using a granola bar and a stapler. We eventually organized our data into a couple of graphs that show the relaptionship between period and mass.   

Data:

Graphs:

Analysis:

Our group created a graph of ln(m + Mtray) v. ln T and found that the value of Mtray was unkown so we plugged in random values into LoggerPro until the correlation of the linear line was as close to the value of 1 as possible. The lower limit came to be 395 grams and the upper limit came to be 440 grams.  

Conclusions:

The power law equation derived in class is an accurate representation of the realtionship between mass and period due to the proportional increase in period and mass shown by the graphs. 

Sources of error in this experiment might have included not placing the masses directly which could lead to an improper and inaccurate reading by the photogate.