University of Chicago
Type of paper: Thesis/Dissertation Chapter
Effect of Force and Mass on Acceleration
Abstract: In this lab there were two principals investigated. The first was the relationship between applied force and acceleration. The second was the relationship between mass and acceleration. To study these two relationships, my partners and I used a dynamic cart with added mass on it. This cart was then attached to a pulley system on a “frictionless track” where it was pulled by a string bearing mass over the edge of a table. In the first relationship tested, applied force and acceleration, mass was moved from being on the cart to being on the end of the pulley. My partners and I measured the acceleration with the LabQuest computer every time the cart was released. In order to test the relationship between mass and acceleration, my group added different amounts of mass to the cart and measured the changes in acceleration. From all of the data collected we concluded that force and acceleration have a direct, linear relationship. We also determined that mass and acceleration have an inverse, quadratic relationship.
Background: When my lab partners and I started this lab, we came in knowing some background information on what we were doing and the concepts involved. We knew that we had to determine the relationships between acceleration in a system and the net force acting on the system. We also knew that we had to discover the relationship between acceleration and mass in the system. Some major concepts we had to understand prior to the lab were Newton’s Fist Law of Motion, acceleration, net forces, and inertia. Newton’s first law states that an object at rest will remain at rest, and an object in motion will remain in motion, with the same speed and direction unless acted on by an unbalanced force. This is important because we were aware that when an object is moving at constant velocity there is a net force of zero.
This gave my group our basic understanding of acceleration, a rate of change of velocity over time; because we realized that when there is an unequal net force the object must be accelerating/ decelerating. This also allowed my group to understand how net forces work, which is especially important since this lab consists of net forces that are not zero. Because the track the cart rode on was considered to be “frictionless,” my group used our prior knowledge to assume that the only unbalanced force in the system was from the horizontal tension in the string. My groups’ understanding that inertia is an objects’ tendency to stay at rest and resist motion helped us during the lab as well. With this background knowledge we were able to perform the appropriate experiments to gain the correct results for our lab.
Purpose: The purpose of this lab was to determine the relationship between mass and acceleration. Another purpose was to determine the relationship between the acceleration in a system and the net force that is acting on the system. We wanted to deepen our understanding of these relationships by proving already known theories for ourselves.
Hypothesis: If the mass of the cart is kept constant but the net force of the system increases (hanging weight over the pulley), then the acceleration will increase. The acceleration will increase because a larger force will cause the object to move faster. This is because as the forces become more unbalanced in the horizontal axis the easier it is for an object to overcome its inertial tendency to stay at rest. However, if the mass of the cart changes but the force is kept constant, then the acceleration will decrease. This will happen because the heavier the object is the more force needed in order for it to move. Adding mass would increase the object’s inertial tendency to stay at rest.
Procedure: To test the relationship between acceleration and force (constant mass) my lab partners and I set up a metal cart on a metal “frictionless” track. The cart had a string attached to it that ran over a pulley, alongside the edge of the table, where it was connected to a hanging mass (as the above drawing indicates). We hooked up a LabQuest data logger to the track in order to document the carts acceleration while being pulled by the hanging weight. My lab partners and I then placed two 500 gram blocks on the cart in addition to five 50 gram masses. On the end of the string hanging was a 50 gram mass. The cart was then released from its held position on the track, and the hanging weight caused the cart to accelerate. This acceleration was documented by the LabQuest data logger. My partners and I performed three trials and then found the average acceleration.
Once the average acceleration was calculated, we took a 50 gram mass from on top of the cart to the hanging mass. The cart was released and the LabQuest data logger documented this new acceleration. We did this three times as well. My partners and I did this until all of the 50 gram masses were transferred from above the cart to onto the hanging string (6 different forces, 15 different trials). After this was completed we found the applied force by multiplying the hanging mass by 9.8 m/s2 (acceleration due to gravity). We then plotted the points and graphed the data to discover the relationship.
To test the second relationship, mass and acceleration, my lab partners and I used the same cart and pulley set up on the “frictionless” track. We calculated the mass of the cart prior to adding any more mass, which was about 500 grams. Once we discovered this number we added five 500 gram masses to the cart. We released this cart three times, using a constant force, and had the LabQuest document the acceleration. We then found the average acceleration for the 3 kg cart. After, we removed one 500 gram mass from the cart. We released the cart three times with this new mass and found its individual and average acceleration. We repeated these steps until all of the 500 gram masses were removed from the cart, and then tested the cart with no added mass (6 different masses, 18 different trials). Once completed, this data was plotted and graphed, and the relationship determined.