Rotational Motion Lab

Purpose: To experimentally confirm a model for the motion of a cork attached to a string that is rotated about an axis by a wooden rod. The expected height of the cork was calculated based on the rotational speed of the apparatus. This was then compared to the results of spinning the cork at different speeds.

Procedure: The apparatus was set up by professor Wolf. Students were unfortunately careful to avoid by the spinning cork. This did improve the accuracy of the experiment. The time for 10 rotations was measured. A paper flag was moved up slightly each revolution until the paper touched the cork. This height was recorded.

Magnetic Potential Energy Lab

Purpose: To derive an expression for the magnetic potential energy of the glider, based on the distance between the magnet on the glider and the magnet on the track. Once this function is determined, the total energy of the glider will be determined based on the position of the glider and the velocity and mass of the glider.


Procedure: A glider, track and blower were setup. The angle of the track was measured and the distance between the surface of the magnets. This was repeated as the angle was increased. The force of the glider was then calculated based on the angle of the track and the mass of the glider.

This produced the following graph:


The magnetic potential energy of the cart was then derived.

The track was leveled and a motion detector placed at the end of the track.

The glider was gently pushed toward the motion detector and the force of the repelling magnet would push it in the opposite direction.

Conclusion: The kinetic energy of the cart was not preserved in our experiment. On of the reasons for this is that the resolution of the position from the motion detector is not very accurate, especially as the magnetic potential energy starts increasing more quickly as the magnets become closer, this makes the error become larger. The graph did show the KE did decrease as the cart approaches the magnet. The PE increased as the magnets became closer together. This shows that with a more accurate experiment, the energy may be preserved.

Impulse and Momentum Lab

Purpose: The purpose of this lab is to demonstrate that by integrating the force wrt position of an impulse the change in momentum can be found. The change in momentum will be measured based on the mass of the cart and the velocity, the impulse will be measured with a force sensor mounted on the cart.

Procedure: A track was setup and leveled. A motion detector was placed at the end of the cart and set on the narrow angle setting. A force sensor was placed on the cart so that the force was applied inline with the cart. A cart was clamped to the table so that the spring plunger would press on the force sensor. The cart was pushed toward the clamped cart and the data from the sensors was recorded. In a second experiment, the hooked tip of the force sensor was replaced with a nail that was taped on the force sensor so that the head of the nail was on the sensor element. The cart and clamp were replaced with a wooden stand with clay for the nail to hit. The cart was again propelled toward the end of the track and the clay and wood stopped the cart, this time in an inelastic collision.

Data Analysis: This produced the preceding graph. The force measured on the force sensor, was integrated to produce the change in momentum. As you can see the change as the cart changes direction. This change correlates with the impulse provided by the spring and force sensor.

In the runs with the clay and nail, the inelastic collisions, the graph of the force was not as smooth. Oscillations are observed due to the clay not immediately absorbing all the energy of the collision. We chose to integrate the total area, since this would ensure that the entire change in momentum would be captured.

Conclusion: It has been shown that by numerically integrating the force applied to an object, the change in momentum can be found. The error seen in the momentum was largely due to the short time of the impulse and the fact that only approximately 30 samples were taken and integrated, limiting the accuracy of the measurement. Additionally, the spring in the cart that was used as a bumper, to lengthen the time of the impulse and lower the maximum force has losses due to friction in the sliding plunger which relies on the plastic on the cart and plunger as a bushing. There are also minor losses to friction in the cart wheels but since the momentum can be calculated just before the impulse and just after, this should not affect the results, significantly.

Conservation of Energy Lab

Purpose: To demonstrate conservation of energy, using a spring mass system. By determining the spring constant, mass and length of the spring, and the mass of the hanging mass on the spring the kinetic energy and potential energy for the spring and mass can be found, using the position and velocity of the hanging mass. This can then be used to find the total energy of the system and if this is constant, the energy is conserved.

Procedure: A rod was clamped to a lab table with a perpendicular rod extending over the floor. A force sensor was attached to the perpendicular rod. A spring was attached to this and a mass hanger to the spring. A motion sensor was placed directly under the

• Spring Constant: The spring was extended while the force and position were recorded. By plotting the force vs distance and finding the slope of this line, the spring constant was found. The spring constant was determined to be BLANK.
• Conservation of Energy: The mass was pulled down and the spring mass system oscillated while the position and velocity of the the mass was recorded using the motion detector.

Data Analysis: The gravitational potential energy of the spring was calculated by using the fact that the the center of mass of the spring only moved 1/2 the distance of the end of the spring, therefore, GPE=(1/2)*Mspring*g*y. The gravitation energy of the spring was calculated as GPE=M*g*y. The Kinetic energy of the mass was calculated as (1/2)*M*V^2. The elastic potential energy was also calculated as EPE= 1/2K*stretch^2.

Conclusion: The total energy of the system was conserved within 4%. Given the precision of the equipment used, this shows that the kinetic energy was conserved. To reduce the error, better equipment would be needed and a better model would need to be used. This model would take into account the fact that the spring does not have equal stretch over the spring, due to the mass of the spring. Also, the kinetic energy of the spring could be taken into account.