Cart+on+Incline-+Tyler+Myers,+Ji-Won+Park,+and+Amir+Raheem

Title of Lab: Cart on Incline

Researchers: Tyler Myers, Ji-Won Park, Amir Raheem

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

Research: As the diagram shows, the horizontal component of the force, mg, is equal to mg sin θ. Since the object is in equilibrium, we know that f is equal to mg sinθ.

Source: http://simple.wikipedia.org/wiki/Inclined_plane

Hypothesis: As a result of the research, we can predict that the tension of the string is directly proportional to sin theta evidenced by the equation T=migsin θ.

Procedure:

Materials: Wooden board, string, protractor, spring scale, cart, scale

1. Calibrate spring scale 2. Connect cart to the spring scale using string, making sure the reading says 0 N on the flat surface 3. Place cart and scale on the wooden board 4. Raise the board at an incline, taking note of the angle of the board using a protractor 5. Record the tension of the string in Newtons 6. Take the angle of the board measured and find its complementary angle. That is θ. 7. Calibrate spring scale 8. Repeats steps 3-7 for various angles. 9. Weight cart using scale, record, and find experimental tension.

Data: The degrees is measuring the angle theta in the picture. We measured the strength in Newtons (as mentioned above), and to get a straight line we squared the newton value. Data Analysis: The first graph is the effect of the slide measured in Newtons and Degrees. The graph resembles a square root curve
 * Degrees || Newtons ||
 * 2 || 0.1 ||
 * 12 || 0.9 ||
 * 22 || 1.8 ||
 * 3 || 2.6 ||
 * 43 || 3.4 ||
 * 53 || 3.9 ||
 * 65 || 4.3 ||
 * 90 || 4.8 ||

This graph is a representation of sin theta vs force. This graph represents the line of best fit, and is almost linear.

Using the points (0,0) and (1,4.8) we can create a line of best fit. The equation for this line is Y=4.8x.

Conclusion: Our hypothesis was found to be supported by the experiment. The steeper the incline, the more tension there is on the string. This relationship is directly related. The equation to find the tension of the string T=mgsin( θ). The calculated equation means that the line has a slope of 4.8. Putting 0 for the value for Y gives us the y intercept, in this case 0. Our experiment had 0.3% error with the mass of the cart measured to be 491.5 grams. Error could have come from the reading of the spring scale, as the increments of the scale were fairly large. Error could also have come from the accuracy of the angle measurements, which were limited to the human eye, a protractor, and string. This experiment could be improved by using implements that gave more accurate measurements of the force and angle.