Cart+on+incline

Title of Lab: Cart on Incline

Researchers:Peter, Chase, Anish

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: sin( theta ) = (mg x / mg) mg sin(theta) = mg x Because the system is in equilibrium: mg x = T  Therefore: T = mg*sin(theta)

Hypothesis: T = mg*sin(theta) Since sin(theta) and tension are directly proportional, the tension of the string will form a linear relationship with the sine of the angle of inclination, whose slope equals the force due to gravity exerted on the object.

Procedure: __ Variables __** : ** Tension, angle of inclination __ Constants __** : ** Mass of cart, gravity __ Materials: __ Incline board, cart, protractor, force gauge. 1) Obtain an incline board, a cart, a protractor, and a force gauge. 2) Attach one end of a string to the force gauge and the other end to the cart. 3) Make sure the string between the cart and the gauge is parallel to the board. 4) Calibrate the force gauge. 5) Place the board at a random inclination. 6) Measure the inclination using the protractor. 7) Find the force in newtons using the gauge. 8) Record the angle and the force in a table. 9) Repeat steps 4-8 at varying inclinations to get as many data points as you want. 10) Find the mass of the cart.

Data:

Mass of the cart = 497.8g.

Data Analysis: The graph of the angle of inclination vs. tension forms a non-linear trend. To make the the relationship more linear, we must graph tension against the sin of the angle, as shown below.



From this graph, we can determine the slope to be approximately 5N, giving us the equation T = 5N*sin(theta). From our proposed equation, the slope (5N) represents the weight of the cart. Since we measured the car using a triple beam balance to be 497.8g, the actual weight of the cart is approximately 4.883N (.4978 kg x 9.81m/s^2), which is close to our estimated value. Our approximation of the car's mass using the above method is 5N / 9.81m/s^2 = .5kg = 500g. Using our estimated mass and the actual mass of the cart leads to a percent error of about 0.44%.

Conclusion: The data supports our equation we formulated to demonstrate the angle of inclination vs. tension, as graphing tension (T) as a function of the sine of theta results in a linear graph whose slope is equivalent to the gravitational force (mg) of the cart, or to put it into the form of an equation, T=mg*sin(theta).