Cart+on+Incline+by+Yuki+Kurosu,+Tyler+Naughton,+and+Samuel+Shaunak

Title of Experiment: Cart on Incline

Researchers: Yuki Kurosu Tyler Naughton Samuel Shaunak

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 Gravity will go always go down on the object causing for two forms of it in the dimensional analysis: MGy( being equal to the normal force and other vertical forces ) and Mgx( being equal to friction and other horizontal forces). MGy will usually be Mg(sinѲ) because it is the corresponding line to the angle while MGx will usually be MG(cosѲ). Normal force is Perpendicular to the surface causing for on an object for it to go at an angle needing the MG(sinѲ).

MG(sin  Ѳ) is directly proportionate to the angle of incline, as the angle increases so does MG(sin).

sources picture [] [] [|http://.com/mstm/physics/mechanics/forces/inclinedPlane/inclinedPlane.html]

Hypothesis: A force exerted on a cart that is parallel to the incline that the cart is on is directly related to the sine of the angle of inclination, due to the formula: T= mg(sinθ).

Procedure: (Materials: plank, cart, scale, protractor, string, force-meter, surface perpendicular to the ground, chair, wooden blocks, and books)
 * 1) Collect all materials
 * 2) Collect the mass of the cart using a scale
 * 3) Lean the plank on a table or wall that it is perpendicular with the ground.
 * 4) Tie the force-meter to the cart using a piece of string
 * 5) Calibrate the force-meter
 * 6) Using the compass measure the angle formed from the underside of the plank.
 * 7) Calculate the angle of inclination which could be done by subtracting 90 to the angle measure taken
 * 8) Record the angle of inclination.
 * 9) place the cart with its wheels on the plank and measure the force needed to keep the cart at equilibrium (in Newtons)
 * 10) Record data
 * 11) Repeat steps 5-10 with different angles of inclination ranging from 90 degrees to almost 0 degrees ( for higher degrees place the plank on top of the back side of the chair or on the seat with by placing a book and/or wooden blocks, but for lower degrees place the plank at the the floor held up b the foot of the chair).

Data:


 * Angle of Incline (degrees) || Force (Newtons) ||
 * 0 || 0 ||
 * 7 || 0.7 ||
 * 14 || 1.0 ||
 * 20 || 1.7 ||
 * 25 || 2.0 ||
 * 35 || 2.7 ||
 * 40 || 3.1 ||
 * 50 || 3.5 ||
 * 60 || 3.6 ||
 * 66 || 4.1 ||
 * 75 || 4.5 ||
 * 90 || 4.8 ||

Data Analysis:



The trend of the data on the Force vs Angle of Incline graph indicates the relationship between Force and the Angle of Inclination is a direct relationship because a line of best fit can be made. The second graph displays the direct relationship between T and mgsin Ɵ. By finding the slope of the sin(θ) vs force graph, which was done by finding the rate of change between two points on the line, the mg can be determined. In this experiment the mg was 4.8 N. The y intercept can be used to determine what the mg would be at no incline and no tension; in this experiment, the y intercept approximates at 0 N.

Conclusion:

The data found on the relationship between tension force and angle of incline shows a direct relationship. Similarly, the relationship between the force of the Cart and the angle of incline is a direct relationship. Proven by our graph, T and mgsin Ɵ have a positive direct relationship with each other , thus verifying our hypothesis that T=mgsin Ɵ.

The slope of the sin( θ) vs force graph is 4.8 and the mg used for our experiment was 4.7 (.484kg * 9.81 m/s2) therefore the percent error was 0.2%. Sources that may have created such error include: not calibrating the force-meter under the same conditions, change in perspective when measuring the angle measure, and change in perspective when determining the force of tension. Though the data collected from the experiment was relatively similar to the expected measures, more attention to detail would have further decreased the amount of error. This would include having a consistent perspective when measuring angles and force, and to make efforts to verify the measure with other members of the group. Overall the experiment was successfully delivered and encourages further understanding of the relationship of Newton's Laws of Motion.