\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Solving Force Problems

Start by analyzing the forces in the system. (See Drawing Force Diagrams)

For each column of the tables, write the sum of the elements in that column.

• If the object is stationary or moving at a constant velocity, set each sum equal to zero.
• If the object is accelerating and you know the acceleration, set the sum equal to the mass of the object times the corresponding component of its acceleration.
• If you don't know if the object is accelerating or not, set the sum equal to $ma_x$ or $ma_y$ where $m$ is the mass and $a$ is the unknown acceleration.

If the number of equations is equal to the number of unknowns, then you will be able to solve for all the unknowns using algebra. If there are fewer equations, then you might be able to solve for some of the unknowns, but not all of them.