Theoretical frictional force of a mass going down a ramp

[Marvels]

Homework Statement

So, we did a lab wherein we rolled a 1.001kg cart down a 24.4 degree slope. We used a ticker tape timer and are trying to find the frictional force of the ticker tape timer alone.

The problem is, I can't figure out how to find the acceleration for the equation

Homework Equations

ma = mgsin(theta) - Ff

The Attempt at a Solution

1.001(a) - 1.001(-9.81)sin24.4 - Ff

Do I need to use vectors? Is it just -9.8? If vectors, do I calculate it for the x or y plane?

 

[andrewkirk]

If you assume the acceleration a is constant (which is equivalent to assuming that the frictional force Ff is constant) then you calculate $a$ from your experimental data. If the cart traveled s metres down the ramp in time t, starting from a stationary state, then the relevant equation is $s=\frac{1}{2}at^2$.

 

[Marvels]

Sorry, I neglected to mention that this part of my work is supposed to be the theoretical. Does that change much?

 

[andrewkirk]

Well you have only one equation, with two unknowns: a and Ff. A numeric solution can only be obtained if further information is provided. That could be the value of one of those quantities, or it could be another equation, based on additional information about the physical system. For the latter, it might be via a formula that gives Ff in terms of the mass of the cart, g and the angle of the slope. But what such a formula might be will depend on the details of the experiment.

A non-numeric solution can be obtained for either of a or Ff by just making it the subject of the equation. Then you will have an expression for a in terms of Ff, or vice versa.