Purpose: 1) Compare the theoretical and experimental velocities

of a marble on a loop track. 2) Compare the theoretical and experimental minimum

heights required for a marble to complete a loop on a loop track.

Background: Potential energy on Earth is mathematically related by

the equation U=mgh (U = potential energy in Joules, m = mass in kilograms, g = acceleration due to gravity & h = height in meters).

The minimum height that an object must be released from to complete the loop can be related with the equation h = 2.5r (h = height in meters, r = radius of the loop in meters).

Materials: CPO Science Timer CPO Science Loop

Track (1) CPO Science

Photogate Marble

Cambridge Physics Outlet Physics Stand

Ruler

Procedure:

1) Clamp the end of the looped ramp to the stand mount.2) Measure vertical distance from top of loop to lab table.3) Set up photogate at 20 cm.4) Attach cables from photogate to CPO Science Timer.5) Release the marble at the top of the ramp.6) Record the time elapsed as measured by the photogate.7) Reset the screen by clearing the time.8) Repeat Steps 5-7 for (3) trials.9) Repeat Steps 4-8 with photogate set at 40cm, 68cm,

84cm, AND 99cm.

Data:

Diameter of marble: 0.0191 cm

Mass of marble: 0.0282 kg

Trial 20cm 40cm 60cm 68cm 84cm 99cm

1 0.0132s

0.0091s

0.0077s

0.0076s

0.0090s

0.0114s

2 0.0132s

0.0091s

0.0076s

0.0076s

0.0090s

0.0112s

3 0.0132s

0.0091s

0.0077s

0.0076s

0.0091s

0.0111s

Average of trials

0.0132s

0.0091s

0.0077s

0.0076s

0.0090s

0.0112s

Velocity 1.45m/s

2.10m/s

2.48m/s

2.513m/s

2.10m/s

1.705m/s

Position on loop track (cm)

Distance from lab table (m)

0 0.54720 0.40540 0.26460 0.12368 (Bottom of loop) 0.08784 (Halfway up loop) 0.20599 (Top of loop) 0.308

Position on loop track (cm)

20 40 60 68

84 99

Theoretical Velocity (m/s)

1.67

2.36

2.88

3.0

2.59

2.16

Potential Energy (J)

Theoretical Minimum Height (m)

0.35

0.097

Experiment Height (m) 0.39

0.108

WorkFRICTION (∆Potential Energy)

0.011 J

Analysis/Observations:

Part I:The velocity was greatest at the bottom of the loop

because the majority of the marble’s potential energy had

been converted to kinetic energy at that point. Conversely, the velocity was least at the 20cm mark of the track because the marble had the greatest potential energy compared to all the other points where velocity was measured. The theoretical velocities were higher than the experimentally measured velocities due to the neglect of friction in the respective calculations.

Part II:Friction slowed the speed of the marble so that releasing

marble at the theoretical height needed to complete the loop did not result in the marble actually completing the loop.

Conclusion:The experimental velocity of a marble in a loop was

compared to its theoretical velocity by using the law of conservation of energy, which assures that the potential energy of an object at the loop of a loop will be fully converted into kinetic energy at the bottom of the loop.

The theoretical minimum height that the marble needed to be released was calculated by using the equation h=2.5r, where as the actual height was determined through trial and error. The work done by friction is the differences in potential energy of the marble at select points on the loop, as the law of conservation of energy states that the total amount of energy in an isolated system remains constant over time.