An object is hanging by a string from your rearview mirror.?

While you are accelerating at a constant rate from rest to 25 m/s in 5.7s , what angle does the string make with the vertical?

Answer 1

Horizontal components of the forces are as follows:

T(sin Θ) = ma — call this Equation 1

and the vertical components of the forces are

T(cos Θ) = mg — call this Equation 2

where

T = tension in the string
Θ = angle that string makes with the vertical
m = mass of the object
a = acceleration = 25/5.7 = 4.386 m/sec^2
g = acceleration due to gravity = 9.8 m/sec^2 (constant)

Dividing Equation 1 with Equation 2,

T(sin Θ)/T(cos Θ) = ma/mg

and simplifying the above,

tan Θ = 4.386/9.8

tan Θ = 0.4475

Θ = arc tan 0.4475

Θ = 24.1 degrees

Hope this helps.

Answer 2

Hangin On A String

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