Cart+on+an+Incline+-+Holly,+Saie,+and+Corey

Title of Lab: Cart on an Incline

Researchers: Saie Ganoo, Corey Keyser, and Holly Therrell

Research Question: How does the angle of inclination affect the force parallel to the incline that is required to keep a cart in equilibrium?

Research: Given Newton's Second Law of Motion where the net force of the system is equal to system mass times acceleration, we are given an equilibrium scenario in which there is no acceleration. Therefore the net forces will rather be described as equal to each other rather than equal to the system mass times acceleration.

The below diagram outlines the scenario and the force distribution. In order to find the correct parallel force you also need to manipulate the diagram to construct a force triangle with the original downward mg being the hypotenuse, which is als o outlined in the diagram. [[image:http://farside.ph.utexas.edu/teaching/301/lectures/img485.png width="466" height="226" caption="\begin{figure} \epsfysize =2in \centerline{\epsffile{slope.eps}} \end{figure}"]]

Through the diagram, we are able to easily derive the equation T=mgsin θ.

Hypothesis: As the angle of inclination increases, the force parallel to the incline required for cart equilibrium will also increase as depicted by the equation T=mgsin θ, thus making T directly proportional to sinθ.

Where θ is the angle of inclination, mg is cart mass times gravitation constant (9.81 m/s^2), and T is tension representing a parallel force needed for equilibrium.

Materials: Force spring scale(scaled to both Newtons and Dynes), triple beam balance, 498.5 g four-wheeled cart, DIY protractor (using string and washer), calculator(analysis), approximately 1.5 m. long wood board, wood props to make appropriate angle.

Procedure: 1. First, we measured the mass of the cart by itself. 2. Then, we began the experiment by placing the board at an inclination of 5 degrees from the ground by using the protractor. 3. The force gauge was calibrated and the cart was gently placed on the board so that we could measure the force required to keep it in equilibrium. 4. This was repeated for different degrees of inclination ranging from 0 to 90 degrees. Data: 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 || Force Required to hold cart in Equilibrium 0.0 0.3 1.0 1.2 1.8 2.1 2.4 2.9 3.2 3.4 3.7 4.0 4.3 4.5 4.7 4.8 4.9 4.9 5.0 || Mass of Cart= 498.5 g.
 * Degree of Inclination

Data Analysis

The line of best fit for our data is shown below. The y-intercept of the line is 0, which means that when the angle of inclination is 0 degrees, the tension in the spring is 0 N. Using the points (.60, 2.4) and (.90, 3.8) circled below on the graph, the slope of the line is 4.7 N. This represents the experimental mg (force due to gravity) part of our hypothesized equation T=mgsin θ. With a mass of 498.5 g, our actual mg would be 4.890 N. Thus, our percent error in this experiment is 3.9%. Because of the small percent error, this experiment supported our hypothesis about the relationship between the tension and the angle of inclination.



Conclusion: While our research based hypothesis that the tension needed at equilibrium(T) will be directly proportional to sin(theta) as depicted by T=mgsin(theta) was proven accurate for the most part, some error was probably caused due to not enough data or an error in measuring the data from a possibly incorrectly calibrated force scale which gave us an experimental value that was a little under the theoretical value. The protractor angle measurements were also not perfectly exact, and were only listed to single degrees, thus giving us uncertainty in the accuracy of our angle measure within a couple degrees. In future repetitions of this experiment we could use more exact instruments paired with repetitions at each angle, in order to provide greater data size and more precise values which could help in achieving more accurate data. Our stated equation is useful for all aspects of life, especially for engineers. By using this equation the appropriate angle of inclination can be determined without millions of experiments, allowing for the efficient application of physics in everyday life.