Question

Dana has a sports medal suspended by a long ribbon from her rearview mirror. As she accelerates onto the highway, she notices that the medal is hanging at an angle of 13 ∘∘ from the vertical.What is her acceleration?

Answer 1

Answer:

$2.26m/s^2$

Explanation:

Suppose the tension in the ribbon is T.

The upwards component of the tension = Tcos13

The horizontal component of the tension = Tsin13

The weight of the medal = mg

In a vertical direction, mg is balanced by Tcos13, so mg=Tcos13, so T  = mg/cos13. The horizontal component of T is the force causing m to accelerate.  

$F = ma\\T\sin13^{\circ} = ma$

Substituting T= mg/cos13 gives:

$\frac{mg}{cos13^{\circ}}sin13^{\circ} = ma$

$m$ cancels and you have

$g\tan13 = a\\a=9.81\tan13^{\circ} \approx 2.26m/s^2$