# Newtons Laws and acceleration

1. Oct 29, 2009

### 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

2. Oct 29, 2009

### 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.

3. Oct 29, 2009

### waldvocm

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

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

Is this correct?

4. Oct 29, 2009

### rl.bhat

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

5. Oct 30, 2009

### waldvocm

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

a=T/m a=11.1

6. Oct 30, 2009

### rl.bhat

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