Question

A fuzzy die that has a weight of 1.70N hangs from the ceiling of a car by a massless string. The car travels on a horizontal road and has an acceleration of 2.70m/s^2 to the left. The string makes an angle theta with respect to the vertical, as shown in the figure below. 1) What is the angle theta?

Answer 1

First we calculate the mass of the fuzzy die

`m=(W)/(g)`

m is the mass, W is the weight, and g is the gravity

m=?

W=1.70N

g=9.8 m/s^2

we susbtitute

`m=(1.70)/(9.80)=0.17\text{ kg}`

Then we calculate the force of x

`Fx=0.17(2.70)=0.468\text{ N}`
`Fy=1.70N`

Then we have the next diagram

Therefore for the angle

`\theta=\arctan ((F_x)/(F_y))=arctan((0.468)/(1.70))=15.4\text{ \degree}`

ANSWER

The angle is 15.4°