# Fuzzy dice acceleration

Kharmon7814
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

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

Kharmon7814
Thanks but why does that work. (Where is the Homework forum?)[?] [?]

Ambitwistor
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;).

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Staff Emeritus
$$\begin{equation*} \begin{split} \sum F_x & = T \sin\theta = ma \\ \sum F_y & = T \cos\theta - mg = 0 \Rightarrow T\cos\theta = mg \end{split} \end{equation*}$$
$$\begin{equation*} \begin{split} \tan\theta \equiv \frac{\sin\theta}{\cos\theta} = \frac{T\sin\theta}{T\cos\theta} = \frac{ma}{mg} = \frac{a}{g} \\ \Rightarrow \theta = \arctan(\tan\theta) = \arctan \frac{a}{g} \end{split} \end{equation*}$$