## 9.4: Problem solving steps

We’ll follow the same problem-solving steps as with problems dealing with conservation laws, but this time we’ll add an intermediate step between the drawing and the math:

- Draw a picture.
- Using your picture, draw a
*free body diagram*that represents the forces acting on one particular object.

- Using your picture, draw a
- Using your free body diagram, apply Newton’s second law.
- Solve.

A free body diagram (FBD) is a problem-solving tool that we’ll use to bridge the gap between the very visual and intuitive picture, and the more abstract mathematical representation. To draw a free body diagram, represent your object as a single point, then draw arrows coming from that point that represent the different forces acting on that particular object. You also need to include coordinate axes for reference.

#### Example 9.3

You are designing an elevator and need to determine the tension in the cable. Your elevator will have a mass of 1200 kg (including passengers) at it’s maximum load, and it needs to be able to accelerate at 1.5 m/s^{2}. Under these conditions, what is the tension in the cable?

The drawing should be pretty simple (it’s just a person standing in an elevator), so I’ll start with a free body diagram for the elevator. The elevator, and everything inside of it, is represented by a single point, and all the force acting on it are represented by arrows. In this case, there are only two forces: the tension in the cable, and the weight of the elevator.

##### FBD—Elevator

Note that the acceleration of the elevator *does not* appear on the free body diagram. Remember that acceleration is a description of an object’s motion—not a force—and a free body diagram only shows the forces which are acting.

Now, apply Newton’s second law and solve:

\[

\begin{align*}

F_\textit{net,y} &= ma_y \\

F^T – F^G &= ma_y \\

F^T – mg &= ma_y \\

F^T &= ma_y + mg \\

&= m(a_y + g) \\

&= (1200\ \textrm{kg})(1.5 + 9.81)\ \textrm{m/s}^2 \\

&= 13.6\ \textrm{kN}

\end{align*}

\]

The cable you choose for your elevator must be able to withstand a tension of at least 13.6 kN without breaking.

#### Practice 9.3

#### Practice 9.4

Hint: you don’t need to do any math for this problem.