Question

A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of 3.20° from the vertical because of the car's acceleration. What is the magnitude of the acceleration of the car?

Answer 1

Answer:

a = 0.55 m/s/s

Explanation:

As the car accelerates in forward direction the string will make some angle with the vertical direction

So here horizontal component of the tension force will accelerates the dice in forward direction along with the car

Vertical component of the tension force will balance the weight of the dice

so we will have

$Tcos\theta = mg$

$Tsin\theta = ma$

here we know that

$\theta$ = angle made with the vertical by string

now divide the two equations

$\frac{sin\theta}{cos\theta} = \frac{ma}{mg}$

so we have

$a = g tan\theta$

$a = 9.81 tan3.20$

$a = 0.55 m/s^2$