Newton's Second Law relates to the behavior of objects for which all existing forces are not balanced. It states acceleration is inversely related to mass and directly proportional to the net force. Acceleration is directly proportional to total force and inversely proportional to total mass. It is the fundamental law connecting forces and motion. If the force acting on an object is increased, the acceleration of the object is increased. If the mass of an object is increased, the acceleration of the object is decreased.
Theory (formula):
EXPERIMENT 1
Design:
Research Question: What effect does changing the net force on a system have on the acceleration of the system?
To determine the effect of changing the net force on the acceleration of the system, we will conduct a controlled experiment. The experiment will include testing different hanging masses and measure its acceleration rolling on the track. Although, we will not change the total mass of the system, we will only transfer mass by taking it off the cart, and applying it to the hanger. This will show us the result of the effect of the hanging mass on the acceleration of the system.
Variables:
Independent Variable: Net Force of the system (N) Dependent Variable: Acceleration (m/s/s) Controlling Variable(s): Total mass of the system
Lab Materials + Setup:
Cart Cart Track (minimum 2 meters) String Force Sensor Weights (20g, 50g, 100g, 200g) Pulley Hanger Motion Sensor + LabQuest Mini Force Sensor Computer (LoggerPro)
This is a similar experiment that shows the lab setup and how the 1st and 2nd experiments are carried out.
Procedure:
Step 1: Measure the mass of the system: the cart, the weights, and the hanger. Step 2: Set up the motion sensor on the edge of the track. Step 3: Measure the force of the hanger that is applied to the cart with a force sensor. Step 4: Start the cart at the start of the track and record data on LoggerPro and start the cart moving simultaneously. Step 5: Record the acceleration by calculating the slope of the Velocity vs. Time time graph on LoggerPro. Step 6: Transfer weight from the cart on to the hanger. Step 7: Repeat previous steps for 5-10 trials.
Recorded Raw Data:
Graphical Analysis:
This graph shows the results of the motion sensor trials represented in Net Force vs Acceleration graph. The data collection presents strong linear progression. Acceleration = 1.194 (m/s/s)/(N) - 0.1455 m/s/s
Slope = As the Net Force increases by 1 N, the Acceleration increases by 1.194 m/s/s
Vertical Intercept = -0.1455 acceleration when the Net Force is 0. This is false however because when the Net Force is 0, the acceleration is 0.
EXPERIMENT 2
Design:
Research Question: What effect does changing the total mass on a system have on the acceleration of the system?
To determine the effect of changing the total mass on a system has on the acceleration of a system, we will conduct a controlled experiment. The experiment will include testing different total masses and measure its acceleration on the cart track. By controlling the Net Force, we can determine the effect of mass on acceleration because they will be the only variables tested in the experiment.
Variables:
Independent Variable: Total Mass of the system (kg) Dependent Variable: Acceleration (m/s/s) Controlling variable(s): Net Force of the system (N)
Procedure:
Step 1: Measure the mass of the system (kg). Step 2: Set up motion sensor with LoggerPro with a Velocity vs Time graph. Step 3: Record total mass of the system and release the cart while the motion sensor is collecting data. Step 4: Record the acceleration by calculating the slope of the Velocity vs. Time Graph from LoggerPro. Step 5: Repeat steps for 5-10 trials.
Recorded Raw Data:
Graphical Analysis:
This graph shows the results of the motion sensor trials represented in a Mass vs Acceleration graph. The data collection represents an inversely proportional function.
Acceleration: 0.2573 (kg)/(m/s/s)
Slope: As the mass increases, the acceleration decreases but it gets less steep.
Vertical intercept: No vertical intercept; the mass can never be 0 kg.
Conclusion:
In this experiment, we investigated the effect of net force on the acceleration of a system, as well as the effect of total mass on the acceleration of a system. These experiments investigated Newton's Second Law of Motion. In Experiment 1, we investigated the effect of changing net force on the acceleration of the system. We found that net force and acceleration are linearly related and proportional. In Experiment 2, we investigated the effect of changing the total mass on the acceleration of the system. We found that total mass and acceleration are inversely proportional. Overall, the data collected help proved Newton's Second Law and how it works.
Evaluation of Procedure:
In both experiments, there were areas of uncertainty. Firstly, the most evident area of uncertainty is reaction time. Since the track was very short, we had to stop the cart almost as soon as it had started to move. It was very hard to record the data because we had to react in a very short period of time. In fact, it was practically impossible to get precise and accurate data. Another area of uncertainty was the amount of data being collected. Since the track was very short, the data collected did not have a significant range which made the data less credible. It was also very hard to find the acceleration with such little data points recorded by the motion sensor. The slopes collected from the Velocity vs Time graphs may be inaccurate, as can be seen with the graph from Experiment 2.
Improving the Investigation:
One way to improve the investigation would be providing more area to conduct the experiment. We could have a longer track for more distance covered, as well as a taller height so that the hanger can have more time to fall. It would help provide better values for the acceleration derived from the Velocity vs Time graphs. We would also obtain a better range of data for the lab. Additionally, it would help solve the issue of reaction time. We will have more time to react and record data. Instead of having less than a second to record data, we have a couple seconds to interpret the more accurate data.