UFPM Challenge

In this lab, we used a modified Atwood machine to predict the intersection of a dropping weight which had acceleration and a cart moving at constant velocity along the ground. For an extra challenge, we angled our Atwood machine slightly. The angle of our ramp was three degrees. Our apparatus looks similar to what follows:

We took measurements of the mass of each component of our contraption:

Object	Mass (kg)
Green cart (on floor)	.477
Weight hanging with string	.059
Buggy	.5883
Whole Atwood machine	1.04

Converting masses to Newtons and using our background knowledge, we created a free body diagram  to help us solve our problem.

In order to predict how to make the weight land on the cart, we calculated the time it would take for the weight to drop to the ground. To do this, we measured the total distance that the weight would fall. 

Our work is as follows:

We used our force diagram to find Fnet and used our measurements to find the mass of the Atwood machine. With this information we were able to find acceleration using the equation Acceleration=Fnet/mass. We plugged .509 into the Fnet and 1.04 in for mass, leaving us with an acceleration of .489m/s^2

Because we knew the distance the weight would drop and the acceleration, we used the following method to solve for the amount of time the weight would drop.

We then used a motion sensor to detect the velocity of the cart that was moving along the ground. Once we found the velocity of that cart (which was .119 m/s), we multiplied it by the time in order to find out how far back to start the cart for the intersection to work. We used the equation 

distance=(velocity)(time) to find out that the cart would travel 25.2 cm. We then placed the cart 25 cm away from where the weight would land. We then let both the cart on the floor and the dropping weight go at the same time and videos the result. Our predictions were correct and the weight landed perfectly on our cart! A video of the experiment is posted below.