Effect of Force and Mass on Acceleration

The Effects of Force and Mass on an Object’s 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.

Lab Drawing:

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.

Data Table:
The Effect of Force on Acceleration
Total Cart Mass (with contents) Mass hanging Average Acceleration Applied Force*
1.75 kg .05 kg .224 m/s2 .49 N
1.70 kg .1 kg .474 m/s2 .98 N
1.65 kg .15 kg .759 m/s2 1.47 N
1.60 kg .2 kg 1.027 m/s2 1.96 N
1.55 kg .25 kg 1.520 m/s2 2.45 N
1.50 kg .3 kg 1.760 m/s2 2.94 N
Table 1 – Acceleration vs. Net Force
* Applied force is calculated by multiplying (mass hanging) by (9.8) ΣF = (.05)*(9.8) ΣF = .49 N

Figure 1 –Force vs. Acceleration. Shows positive linear direct relationship

The Effect of Mass on Acceleration
Mass on cart (including mass of cart) Average Acceleration
2.9933 kg .1280 m/s2
2.4933 kg .1734 m/s2
1.9933 kg .2227 m/s2
1.4933 kg .2968 m/s2
.9933 kg .4205 m/s2
0.4933 kg .8313 m/s2
Table 2 – Mass vs. Average Acceleration

Figure 2 –Mass vs. Acceleration. Shows negative quadratic inverse relationship

Conclusion:
There were two purposes in this lab; the first was to discover the relationship between acceleration in a system and the net force acting on the system, and the second was to discover the relationship between acceleration in a system and mass in a system. While testing for the first relationship mass was kept constant, and for the second relationship force was kept constant. The first hypothesis was that if mass was kept constant while the net force of the system increases, then the object will accelerate proportionally to the force increase because a larger force will cause objects of the same mass to move faster. The second hypothesis stated that if the mass of the system increases while force is kept constant then the object will decelerate because it takes more force to accelerate heavier objects and have them resist their inertial tendencies.
My hypothesis is supported by the results of this lab. When looking at figure 1, it is evident that the graph reflects a positive, linear trend. This shows a direct relationship between force and acceleration in a system, meaning that force and acceleration increase together. For example, at .49 N of force the average acceleration was .224 m/s2. At 2.94 N of force the average acceleration was 1.760 m/s2. This shows a 1.536 m/s2 increase over a 2.45 N of force increase. This increase supports the idea that when mass is kept constant, more force will lead to a larger acceleration. In addition, the second part of my hypothesis is supported as well. Mass and acceleration do have an inverse relationship; however I did not predict that the relationship would be quadratic. When the mass on the cart was about .5 kg the average acceleration was the largest at .8313 m/s2. When the mass on the cart was about 3 kg, the acceleration was the slowest, at .1280 m/s2. This obviously shows the negative trend of the relationship. After graphing all the data, I noticed the negative quadratic trend as figure 2 shows.
My lab partners and I are very confident in our results; however there are some minimal validity issues that we experienced. The largest issue was the inconsistency of the releasing of the cart. My partners and I did not release the cart at the same spot on the track every time, which could have skewed our results in a minimal way. During some trials the cart was on the track for a much longer period of time than others. I do not think that this issue had a profound effect on our results, and that they can still be trusted. The three trials we performed should have eliminated most of these issues and given us the correct average accelerations. Another factor that affected our results was the fact that the “frictionless track” was not completely “frictionless.” There was a little friction between the wheels of the cart and the track, but it was very minimal and consistent for all trials. This did not really affect our data at all. This friction was insignificant to the lab results. Finally, one last issue with the lab was the height of the pulley over the table. For the most part my lab partners and I kept the pulley level with the height of the cart, but as we performed more trials the pulley accidently got pushed and may have shifted position a little bit. I believe that this is also an insignificant problem that did not affect our results. Overall, I believe that our results can be trusted. Our hypotheses were supported by the data and our results match the expected results according to Newton’s Second Law of Motion.