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.