We're asked to determine the **angle *** θ *from the vertical and

Anytime we have a problem with multiple objects accelerating together, we know it's a **system-of-objects** type problem. We'll follow these steps to solve:

- Draw a
**free-body diagram**for each body we're interested in - Write Newton's Second Law equations
**∑**, noting that*F*=*ma**a*is the same for both - Solve for the
**target variable**

Obviously, we'll be using the equation for Newton's Second Law:

$\overline{)\begin{array}{rcl}\mathbf{\sum}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}& {\mathbf{=}}& \mathit{m}\stackrel{\mathbf{\rightharpoonup}}{\mathit{a}}\end{array}}$

We may need our equations for decomposing vectors:

$\overline{)\begin{array}{rcl}{\mathit{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{F}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

And those for determining the magnitude and direction of a force from its components:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{F}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{F}}_{\mathit{y}}}^{\mathbf{2}}}}$

$\overline{){\mathbf{tan}}{\mathbf{}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{F}}_{\mathit{y}}}{{\mathit{F}}_{\mathit{x}}}}$

An object of mass *m* = 0.500 kg is suspended from the ceiling of a truck accelerating at a constant rate on a straight, level road. Taking *a* = 3.00 m/s^{2}, find:**(a)** the angle *θ* that the string makes with the vertical**(b)** the tension *T* in the string.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Systems of Objects: Basic concept. If you need more Systems of Objects: Basic practice, you can also practice Systems of Objects: Basic practice problems.