Mechanics - Forces and Motion

What is a force diagram?

A diagram showing all the forces acting on an object.

What should you draw whenever you have a problem involving forces in Mechanics?

A force diagram.

In $\hat{i}$ and $\hat{j}$ notation, what is the value of a resultant force for an object in equilibrium?

\[0\hat{i} + 0\hat{j}\]

If

\[\left(\begin{matrix} 2+p \\ 5+q \end{matrix}\right)\]

is parallel to

\[\left(\begin{matrix} 1 \\ -2 \end{matrix}\right)\]

, what equation could you write in terms of a new variable $k$ to aid in solving?

\[\left(\begin{matrix} 2+p \\ 5+q \end{matrix}\right) = \left(\begin{matrix} k \\ -2k \end{matrix}\right)\]

If

\[\left(\begin{matrix} 2+p \\ 5+q \end{matrix}\right) = \left(\begin{matrix} 1k \\ -2k \end{matrix}\right)\]

is true, what two equations can you write?

\[2+p = k \\\\ 5+q = -2k\]

\[2+p = k \\ 5+q = -2k\]

How could you rewrite this so it’s just in terms of $p$ and $q$?

\[-2(2 + p) = 5 + q\]

What’s the normal procedure for answering a ladder or hinge question?

How many components of reaction are there at a wall in a ladder question?

\[1\]

How many components of reaction are there at the hinge?

\[2\]

Why is the reaction on a smooth surface always perpendicular to the surface?

As the surface is smooth, there is no friction and so the reaction is unchanged.

When reading a tricky mechanics question, what is it a good idea to do?

Circle all words like “smooth”, “rough”, “uniform”, etc.

Is the reaction force necessarily the resultant force?

No, not if there is friction involved.

If a string connecting two particles over a pulley is not actually light, what will be true?

The tensions will no longer be equal.

See Also