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

`2.26m/s^2`

Step-by-step 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:

`(mg)/(cos13^(\circ))sin13^(\circ) = ma`

`m` cancels and you have

`g\tan13 = a\\a=9.81\tan13^(\circ) \approx 2.26m/s^2`