Lab partners: Adithya Kalyan, Edward Li, Andy Chen
Date: October 26th, 2021
How does the acceleration of an object depend on the mass or net force acting on object?
Net Force Lab Independent Variable: Mass on hanger
Mass Lab Independent variable: Total mass of system
Dependent Variable of both labs: Acceleration of the cart
Controls for Net Force Lab: Total mass of system, Cart, ramp, pulley, sensor
Controls for Mass Lab: Mass of hanger, cart, ramp, pulley, sensor
Controlling Variables: For the Net forces lab in order to get an accurate measurement in a controlled environment, we will always have the same cart running on the same ramp. We will make sure that there is no obstacles on the ramp so that nothing will interfere with the speed of the cart.
Developed Method for Collection of Data
Net force Lab:
For this lab we will keep the total mass of the system constant at 1.680 kilograms. What we will be changing through this experiment is the allocation of the weights. For example we will start with 1.63 kg on the cart itself and each trial take one weight off and put it on the hanger to see how this will affect the acceleration. To collect the data Andy will be with the computer and he will start the sensor's data collection and as soon as he does that Edward will let go of the cart. Adithya will be on the other side of the ramp and will stop the cart right before the hanger hits the ground so as to ensure that the data we get isn't scrambled.
Mass Lab:
For this lab we will change the total mass of the system by increasing the amount of weight on the cart itself. We will not be changing the weight on the hanger because this has to be constant for a good experiment. Each trial we will add 100 grams to the cart and see how this affects the acceleration of the cart on the ramp. To collect the data we will have a similar process to the Net Force lab where Andy will initiate it by pressing the collect data button on his computer and as he does this, Edward will let go of the cart. Adithya will stop the cart before the hanger hits the ground to make sure we won't have bad data at the end.
Procedure
Using a sensor, we measured the acceleration of the cart as it went down the ramp in response to differing amounts of weight on the cart and hanger.
Only ran 6 trials for Net Force Lab but ran 13 trials for the Mass Lab
Lab Setup
Recorded Raw Data
*environment constant*
*pulley constant*
*cart constant*
Net force Lab: Total mass of system constant (1.68 kg)
Mass Lab: Mass of hanger constant (0.05 kg)
Processed Raw Data
We processed our data correctly because we had a sensor that created a graph of the acceleration of our cart so we were not doing this by hand. Although there is room for error when the hanger hits the ground since there is no longer the same amount of mass on the other side of the pulley, we eliminated this error by only analyzing a line of best fit for the part of the graph that seemed to follow a pattern and had strong linear association. Also since we only used the slope of the line of best fit as our data point, it is an average and there is room for error there. One possible fault is the software that we used. The software could have glitched but we still believed it.
Net Force Lab
Line of best fit: y = 0.5733x
slope interpretation: Acceleration increases by 0.5733 for every Newton increase in net force
Increasing Mass Lab
Line of best fit: 0.5095x^ -0.9213
slope interpretation: The acceleration will exponentially decrease as the amount of mass added to the cart increases
Final Results
The evidence shows that as the Net Force acting on the cart increases, the acceleration of the cart will increase linearly. We know this because the line of best fit is proportional for the net force acceleration graph. The reason it is proportional is because when there is no net force acting on the cart, the cart will not be moving so there can not be any acceleration. The slope of this graph is positive 0.5733 meaning that it is constantly increasing at a set rate. We can generalize this information to mean that whenever the larger the net force acting on an object, the larger the acceleration of the object.
The second data set shows that as the Mass of the object increases, the acceleration of the object will exponentially decrease. We know this because the power graph has a negative exponent meaning that it is a decreasing exponential graph. The heavier an object is, the more force it requires in order to move it. We can generalize this information in other scenarios to see that it would be exponentially harder to move a car than it would be to move a bike and that it is not a linear association
Conclusion
We know that the inertia of an object is its tendency to resist a change in motion as per the Law of Inertia. We also know that the inertia of an object is solely based on the mass of an object. Newton's first law states that an object will continue to travel at a constant velocity until it feels an unbalanced push or pull. In this unbalanced forces object there is always an unbalanced force acting on the object as the hanger is always moving and is attached to the cart by a string so its always accelerating. As this lab showed, the larger the mass of an object, or the larger the inertia, the harder it is to make it change its current state of movement. For example during this experiment a 0.50 Newton net force took much longer to get a 2430 gram cart to the same speed as a 530 gram cart. This experiment also showed that the larger the force acting on an object, the easier it will be to move that object. The larger the net force of the hanger was in the net force object, the faster the acceleration became. Because we used a computer software and a sensor to calculate the acceleration of the cart, there is little room for error but that should be taken into account as a possibility as well. From this experiment, I learned about inertia and net forces and how these affects its acceleration. I also learned how acceleration has a direct relationship with net force and mass. We derived the equation that a = net force/mass. This equation is really useful because you can find the acceleration, net force, mass, gravity, and normal force acting on an object using it. It really opens up a lot of physics.
Evaluating Procedure
When we did this experiment on a couple of the trials, the hanger hit the ground before the cart was stopped. Although we only fit a line of best fir for the part of the graph that showed strong linear association, some bad data could have slipped in and made things inaccurate. Another weakness of our lab is that for the Net force lab we only did 6 trials which is not a large enough sample size too get very accurate data. However I think that an extra 4 trials would only affirm the results that we got with our first 6 trials. We also made the assumption that the sensor did not malfunction and was giving us accurate data. If the sensor was not giving us the correct data the entire lab would be innaccurate.
Improving the Investigation
One possible improvement for our lab is the length of the experiment. The distance of the hanger off the ground was not much at all so it hit the ground really fast. This greatly limited our data set size because we had to stop the cart quickly in order to beat the hanger. If the ramp was farther above the ground, than we would have more time and more data to get a more accurate acceleration. Another basis for improvement is the number of trials for the net force lab. If we had more trials we would have more data to create a better line of fit. Also we created a proportional line of best fit for our net force lab instead of a linear fit because when we fit a linear line of best fit we got a y-intercept of -0.001089 which is impossible however the difference from 0 is so little it makes little difference.