Mechanics - Forces and Motion

Pearson Edexcel Mathematics 2022


See Also

Flashcards

Force diagrams and equilibrium

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?

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

Parallel vectors and solving for unknowns

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 $q$?

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

Ladder and hinge questions

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

  • Take moments
  • Resolve forces

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?

\[2\]

Reactions, friction and reading questions

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.

Pulleys and strings

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

The tensions will no longer be equal.