How Does a Car's Acceleration Affect the Angle of a Hanging Air Freshener?

[waldvocm]

The pine tree air freshener hanging from the rear view mirror makes an angle of 27.9 degrees with the vertical while a car is acceleration

a)What is the car's acceleration

ax=gsin(theta)=9.80*sin(27.9)=4.59

b)What is the tension in the string of the 100g air freshener?

ax=T/m=4.59(100)=T

T=458 (Or does the mass always have to be in kg?) T=.458

 

[rl.bhat]

According to the law of inertia, when the car moves forward with an acceleration a. the freshener moves with the same acceleration in reverse direction. If T is the tension in the string, them in the equilibrium condition
ma = T*sinθ and mg = T*cosθ. Here m must be in kg.
Now solve for T and a.

 

[waldvocm]

.10=T(cos(27.9)) T=.11315

.10a=.11315(sin(27.9)) a=.529

Is this correct?

 

[rl.bhat]

.10=T(cos(27.9)) T=.11315

.10a=.11315(sin(27.9)) a=.529

Is this correct?

No. It is not correct.
0.10*g = T(cos(27.9))

 

[waldvocm]

.10(9.80)=T(cos(27.9)) T=1.11

a=T/m a=11.1

 

[rl.bhat]

Write down the units.
Check the calculations. T*sinθ = ma.