Cart+on+Incline-+Daniel,+Charlie,+Joey,+and+Kevin

__**Title of Lab:**__ Cart on Incline Lab

__**Researchers:**__ Daniel Hicks, Charlie Morris, Joey He, Kevin Sarfani

__** 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**__: Since this situation is at equilibrium, the upward forces are equal to the downward forces and the leftward forces are equal to the rightward forces. So based on the free body diagram, the friction force will be equal to the force needed to keep the cart in equilibrium. This force can be found by using the formula mgsin ** Θ. **

https://www.cdli.ca/sampleResources/physics3204/unit01_org02_ilo03/u01-s02-ls03-lessonfig05.gif (free-body diagram found at this website.)

Represented by the expression T= mgsin ** Θ **
 * Hypothesis: ** The greater the angle the more force needed to keep the cart at equilbrium. The sine of the angle of incline is directly proportional to the force needed to keep the cart in equillibrium.

__** Procedure: **__ Materials: wooden board(used for incline), force gauge, 497.3 g cart, protractor with string and weight attached(used to measure angle), triple beam balance

1.Pull string up to calibrate the force gauge to 0 N 2. Attach the force gauge to the cart 3. Raise wooden board (the incline) to a certain angle and record the degrees 4. Record force at that angle 5. Repeat steps 1-4 at numerous angle measurements to get more information 6. Measure mass of cart with the triple beam balance

__** Data: **__
 * Angle(in degrees) || Force(N)  ||
 * 5 ||  .4  ||
 * 11 ||  1.0  ||
 * 13 ||  1.0  ||
 * 20 ||  1.6  ||
 * 21 ||  1.6  ||
 * 30 ||  2.3  ||
 * 38 ||  3  ||
 * 44 ||  3.4  ||
 * 50 ||  3.5  ||
 * 55 ||  4  ||
 * 65 ||  4.2  ||
 * 78 ||  4.8  ||
 * 80 ||  4.8  ||
 * 90 ||  5  ||

__** Data Analysis: **__

Data plotted: This graph shows the relationship between angle inclination and tension(N). The graph begins to curve so in order to make the graph linear, we plotted the sine of the angles from the experimental data. Then we created a line of best fit.

The values for sin θ° are directly proportional to the force in Newtons (N). Using the points (.62,3) and (.5, 2.4) we found the slope of the line of the line to be 5 N/ degrees, which represents the force due to gravity of the cart. The y-intercept is at (0,0) meaning that at 0 degrees, there is 0 newtons of force.

By using the graph of Tension v sin ** Θ, **we showed that the sine of the angle of incline is directly proportional to the force needed to keep the car in equilibrium, so our hypothesis T=mgsin ** Θ ** is supported by the test data. The theoretical slope was 4.9 N/degrees based on the 497.3 weight of the cart. Our experimental slope is 5 N/degree so there is around a 2% percent error. This could be reduced by using a more accurate protractor and having something more stable to hold the wooden board in place.
 * Conclusion: **