Theoretical frictional force of a mass going down a ramp

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Homework Help Overview

The discussion revolves around a lab experiment involving a cart rolling down a slope, where the original poster seeks to determine the theoretical frictional force acting on the cart. The subject area includes concepts of dynamics, specifically relating to forces, acceleration, and friction on an inclined plane.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply Newton's second law to find acceleration but questions whether vectors are necessary for the calculations. Some participants suggest calculating acceleration from experimental data while considering the assumption of constant acceleration.

Discussion Status

The discussion is ongoing, with participants exploring the implications of theoretical versus experimental approaches. There is recognition that the original poster's problem involves two unknowns, leading to the need for additional information or equations to progress further.

Contextual Notes

Participants note that the original poster's focus on theoretical aspects may influence the approach to finding the frictional force. The need for further information or equations to resolve the two unknowns is emphasized.

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

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