1. Dynamics of Moving Objects in Kinetic Sculpture (Ball Drop Physics II)
COSMOS LECTURE
Dynamics of Moving Objects in Kinetic Sculpture (Ball Drop Physics II)
Main title of program. Perhaps worth mentioning is that I work at the Dynamic Systems & Control Group at the Dept. of Mechanical and Aerospace Engineering at UCSD. But most of this work is done at the Center of Magnetic Recording Research at UCSD
Raymond de Callafon
Dynamic Systems & Control Group
Center of Magnetic Recording Research
UCSD, Dept. of MAE
UCSD - R.A. de Callafon
July 18, 2007

2. Physics in Kinetic Sculpture
Observations:
main force acting on balls: gravity
pendulums create “randomness”
conversion of potential energy to kinetic energy
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

3. Energy in Kinetic Sculpture
Energy Conservation:
Motor + “ball elevator” increases potential energy
Ball rolling down slides converts potential energy into kinetic energy
Energy loss during conversion due to:
Friction of balls on slides
Loss of energy while balls bounce (trampoline or in baskets)
Friction of air while balls move …
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

4. From Last Lecture: Ball Drop
End Velocity of Ball Drop
potential energy = kinetic energy
potential energy P of mass M height h:
kinetic energy E of mass M with velocity v:
conservation of energy yields:
y(t) M
F(t) h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

5. From Last Lecture: Ball on a Ramp
End Velocity of a Rolling Ball
potential energy P of mass M at height h:
kinetic energy E of rolling M with velocity v:
conservation of energy yields end velocity of rolling ball:
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
Note: 10/7 is smaller than 2! h
UCSD - R.A. de Callafon
July 18, 2007

6. Ball Falling from Ramp End Velocity of a Rolling Ball
With the solution we can compute the end velocity of the ball on a ramp (no friction)
What happens if ball leaves ramp?
Ball falls on trampoline
Balls fall in basket
Approximate position of ball needed for placement of trampoline, basket, etc. in Kinetic Sculpture…
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

7. Ball Falling from Ramp
As soon as ball leaves ramp: constant velocity in X-direction, linear increasing speed in Y-direction!
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

8. Ball Falling from Ramp
As soon as ball leaves ramp: constant velocity in X-direction, linear increasing speed in Y-direction.
Why?
When ball leaves ramp, only force on ball is gravity force in Y-direction
This results in:
Ball remains its velocity v in X-direction!
Ball’s velocity in Y-direction is described by vertical drop of ball: v=gt
vx(t)=v
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
vy(t)=gt
UCSD - R.A. de Callafon
July 18, 2007

9. Ball Falling from Ramp Jump Distance of a ball h
How to determine the distance d, given the height difference h of the ramp and the jump height y? h y
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive. d
UCSD - R.A. de Callafon
July 18, 2007

10. Ball Falling from Ramp Jump Distance of a ball
Height h determines the end velocity of the rolling ball leaving the ramp.
What is the end velocity vx?
Jump Distance of a ball d y h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

11. Ball Falling from Ramp Jump Distance of a ball
Jump height y determines how long it takes for ball drop and reach the ground.
What is the time t before its reaches the ground?
Jump Distance of a ball d y h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

12. From Previous Lecture Vertical Drop of Ball With solution:
(re)consider the question:
How long does it take (at what time t) to reach the ground at height h ? M
y(t)
F(t) h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

13. Ball Falling from Ramp Jump Distance of a ball
Jump height y determines how long it takes for ball drop and reach the ground.
What is the time t before its reaches the ground?
Jump Distance of a ball d y h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

14. Ball Falling from Ramp We have: Jump Distance of a ball
Travel distance d is determined by time t before ball reaches ground.
What is distance d?
Jump Distance of a ball d y h
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

15. Ball Falling from Ramp Jump Distance of a ball h y d
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive. d
UCSD - R.A. de Callafon
July 18, 2007

16. Bouncing of Balls
After ball bounces at distance the impact is an important factor in loss of (kinetic) energy.
Effect of bounce is modeled by coefficient of restitution. d
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

17. Bouncing of Balls Coefficient of Restitution
The coefficient of restitution (denoted by the symbol c) is a measure of the elasticity of a collision.
The coefficient of restitution is the ratio of the velocities before and after a collision: where v2 is velocity after collision, v1 is velocity before collision
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

18. Bouncing of Balls Coefficient of Restitution
Consider the example of a simple ball drop:
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

19. Bouncing of Balls Coefficient of Restitution
Consider the example of a simple ball drop
For a ball drop we have:
A low coefficient of restitution means a large (kinetic) energy loss during the collision.
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

20. Bouncing of Balls Coefficient of Restitution
In case of a ball drop, the coefficient of restitution c can also be measured by difference in bouncing height of a ball.
For a ball drop we have: where h2 is ball height after the bounce, h1 is the ball height before the drop.
A low coefficient of restitution means a large (potential) energy loss during the collision.
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

21. Physics Lab II Ball Jump Experiment
Create experiment to measure ball jump
Measure ball jump distance d and compare with theory
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007

22. Physics Lab II Coefficient of Restitution
Create experiment to measure coefficient of restitution of trampoline
Measure coefficient of restitution c and simulate behavior with a Working Model 2D model
Pretty self explanatory. Main motivation of this work is to develop news tools (software, hardware and principles) to evaluate the servo performance of a (LTO) drive. The tools will consists of the 4 bullets mentioned above. The tools are focused on experimental analysis of data that can be measured from the servo loop in the drive. Subsequently, the analysis results can be used within the scope of designing enhanced servo system for a tape drive.
UCSD - R.A. de Callafon
July 18, 2007