# Fuzzy dice acceleration

I'm not sure I have enough info but the question goes like this...Fuzzy dice are hanging from a rearview mirror. The car accelerates at 3.54m/s^2 What angle will the dice make with the vertical? I have a force diagram showing of the dice Mg points down. T points up to the right in the 1st quadrant. For the summation of forces I have Fx=Tcos(theta)=M(3.54m/s^2) and Fy=Tsin(Theta)-Mg=0. What am I missing? Not sure how to find theta..Thanks

Divide the two equations and take the arctangent. (And post in the homework help forums.)

Thanks but why does that work. (Where is the Homework forum?)[?] [?]

If you divide the two equations, the T's cancel out and you get a sine divided by a cosine, which is a tangent. The arctangent inverts the tangent in order to solve for the angle (arctan(tan(&theta;)) = &theta;).

The Homework Help Zone is near the bottom of the main physicsforums.com page.

chroot
Staff Emeritus
Gold Member
Ambi,

Do me a favor and try using some of the LaTeX code! :)

- Warren

$$\begin{equation*} \begin{split} \sum F_x & = T \sin\theta = ma \\ \sum F_y & = T \cos\theta - mg = 0 \Rightarrow T\cos\theta = mg \end{split} \end{equation*}$$

$$\begin{equation*} \begin{split} \tan\theta \equiv \frac{\sin\theta}{\cos\theta} = \frac{T\sin\theta}{T\cos\theta} = \frac{ma}{mg} = \frac{a}{g} \\ \Rightarrow \theta = \arctan(\tan\theta) = \arctan \frac{a}{g} \end{split} \end{equation*}$$

Last edited: