- #1

srekai

- 8

- 0

**I did the problem, just want to validate my solution/approach**

1. Homework Statement

1. Homework Statement

Your car happens to have a fuzzy die hanging from the rear view mirror. As you round a curve that is approximately a circle of radius R you notice that the fuzzy die makes an angle θ with the vertical. What is the angle θ as a function of R and your speed v?

## Homework Equations

$$\sum F = ma$$

$$F = \frac{mv^2}{r}$$

## The Attempt at a Solution

There are 3 forces on the dice as shown in the free body diagram attachment

From this the sum of the vertical forces and horizontal forces must cancel out, so we can say

$$F_{\text{tension,y}} = F_{\text{gravity}}$$

$$F_{\text{tension}} \cdot cos \theta = F_{\text{gravity}}$$

$$F_{\text{tension}} \cdot cos \theta =mg$$

$$F_{\text{tension}}= \frac{mg}{cos \theta}$$

and

$$F_{\text{tension,x}} = F_{\text{tangential}}$$

$$F_{\text{tension}} \cdot sin \theta = F_{\text{tangential}}$$

$$F_{\text{tension}} \cdot sin \theta = \frac{mv^2}{r}$$

$$ \frac{mv^2}{r} = mg \cdot \frac{sin \theta}{cos \theta}$$

$$tan \theta = \frac{v^2}{rg}$$

$$\theta = tan^{-1}\frac{v^2}{rg}$$

#### Attachments

Last edited: