Cart+on+Incline-+Anand,+Swathi,+Nick+6th

= Title of Lab: Cart on Incline =

Researchers:
Swathi Ganesh, Nick Gant, Anand Rajagopal

**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:
The force parallel to the incline of a ramp is equal to the weight of the cart (in Newtons) multiplied by sin θ (θ being the angle of inclination) as demonstrated by the diagram below. As θ increases sinθ increases (for values of θ between 0° and 90°).



Hypothesis:
The force parallel to the incline that is required to keep a cart in equilibrium is directly proportional to the sine of the angle of inclination of the surface.

Materials:
force gauge, wooden plank (to use as incline), cart (with string attached to attach force gauge), protractor (with attached string and weight), triple beam balance (to measure mass of cart)

Pr ocedure:
(1) Find the mass of the cart by placing it on the triple beam balance. (2) Calibrate the force gauge so that the reading is at 0 Newtons and calibrate the protractor so that the string is at 90 degrees. (2) Start by placing the plank on the ground at zero degrees and measure the tension by attaching the force gauge to the cart and holding the force gauge. Make sure that the angle at which you are holding the force gauge is parallel to the inclined surface. (3) Raise that plank at an angle with one end of the plank touching the floor and the other end being held by someone or placed on another surface. The angle can measured by placing the straight edge of the protractor under the inclined surface. Then, hang the cart onto the force gauge as you did in step 2. (4) Do this for various angle measures until you reach 90 degrees.

Data Analysis:
__// Force vs. Angle of Inclination //__

__//Force vs. Sine of the angle of inclination//__

The slope of the best fit line based on our data suggest that the slope for a force vs. sin( θ) relationship is equal to the weight(mg) of the object to which the force is acting upon. Our experimental value for the slope of the best fit line is approximately 4.66 N, while the theoretical value is 4.81 N, giving us a percent error of -3.1%. This error could have been caused by a limited amount of precision of the instruments used to measure both the angle of the incline and the force. Adding to our percent error could have also been our disregard to do multiple trials at the same measurements. We also failed to calibrate our force gauge before measuring the force at each of our different angle measures, which could have also contributed to the error. The significance of the y-intercept, in this case, 0 N, is that this is the only sure point on the graph in that it does not have an error because when an object is at rest on a flat surface, it does not exert any force, unless acted on by an outside force (Newton's First Law of inertia). We can use this point as a starting point for our line of best fit, which will help us to derive a more accurate best-fit line, and therefore, slope.

**Conclusion:**
The hypothesis was supported by the evidence. As the angle of inclination increased (from 0 degrees to 90 degrees), the force needed to keep the object in equilibrium increased in smaller increments (represented by a sine curve). Thus, plotting sine of the angle of inclination vs. the force, a linear relationship could be derived. The line of best fit drawn with the data justifies the relation between the slope of an incline and an object's mass, giving us the equation F=weight*sinθ or F=4.81sinθ. In order to improve our experiment, we would've used more precise instruments for measuring while also carrying out multiple trials to help increase the chance of obtaining accurate and precise results.