Cart+on+Incline-+Jordan+Anderson,+Aaron+Floyd,+Peyton+Coleman

Title of Lab: Cart on Incline Plane

Researchers: Jordan Anderson, Aaron Floyd, Peyton Coleman

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: Newton's Second Law states that the sum of the forces is equal to the mass times acceleration. Since the situation is at equilibrium, the acceleration is at zero. This means that the net force must also equal zero. Since the cart is on an incline, the force of gravity must be split into mgx and mgy. Since the cart is at equilibrium, the upward forces must equal the downward forces, and the leftward forces must equal the rightward forces. Therefore, mgx=F, or mgsin θ=F. The variables for this experiment are force and the angle of inclination. The constants are gravity and the weight of the cart.

Hypothesis: The parallel force increases as the angle of inclination increases using the formula F=mgsin θ where F is the parallel force, or tension, pulling the cart back up the incline. The force is directly related to sinθ.

Procedure: 1) Get a board, cart, force gauge, string, protractor, and balance. 2) Calibrate the balance and force gauge. 3) Use the balance to weigh the cart 4) Attach the string to the cart and force gauge. 5) Set up the board at a specified angle. Use the protractor to find the angle. Then find the angle of inclination by finding the complimentary angle. 6) Place the cart on the board and let it go. 7)Look at the force gauge to determine the force pulling on the cart in Newtons. 8) Repeat steps 2 for the force gauge and 5-7 at different angles of inclination. 9) Record results in a chart then graph. Data:
 * Angle of inclination (degrees) || force in Newtons ||
 * 0 || 0.0 ||
 * 10 || 0.9 ||
 * 20 || 1.3 ||
 * 30 || 2.2 ||
 * 40 || 2.8 ||
 * 50 || 3.4 ||
 * 60 || 4.0 ||
 * 70 || 4.5 ||
 * 80 || 4.6 ||
 * 90 || 4.9 ||

Data Analysis: This graph is a Force vs angle of inclination graph of the data we recorded during the experiment. You can see how as the angle increases, the force increases. However, this does not form a perfect line. This graph is a tension vs sin θ graph. This graph helps give us a straight line to show the relationship between sinθ and the force. The slope of the line is 4.9N. The slope represents the force of gravity (mg) in our hypothesized equation. The y-intercept is 0. This means that at a 0 degree angle, the force would be 0 Newtons. Our percent error was 2.0%. This was most likely due to human error when measuring the angles and the way we held the force gauge and read it.

Conclusion: The data we collected supported our hypothesis because as sin θ increased, the force increased. Thus, sinθ is directly related to the force. To improve this experiment, we could have tested for more angles to increases our data's accuracy, and we could have done more than one trial for each angle to be more precise.