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.