The acceleration of the cart and weight in the incline plane

The acceleration of the cart and weight in the incline plane experiment is given by

Where m1 is the hanging weight mass, m2 is the cart mass, M is the total mass, is the angle of inclination, g is the local acceleration due to gravity, and R is the sum of all resistive forces.

When the angle of inclination is small, the small angle approximation can be made

Where is in radians.

An incline plane experiment is done with a cart that has a mass of 500 grams, a hanging weight with a mass of 100 grams, and the experiment is done on Earth where g = 9.80 m/s2. A group of students perform the incline plane experiment with the above parameters and measure the acceleration of the cart for several angles of inclination. They plot their data, and then perform the LINEST function. They find that for their data set that the y-intercept is equal to 1.52 m/s2. Use the y-intercept to estimate the magnitude of the resistive forces. Answer in newtons, and to the fourth decimal place. Please be as detailed as possible, I\'m really stuck on this one. The answer is NOT 0.76N nor is it 40N.

Solution

The y-intercept as evident from the equation is given by -R/M

So R=-ym*M = -0.6*1.52=-0.912N

So the magnitude is given by 0.912N