Question

A model plane with a fan motor is hanging from the ceiling by a string, and it is spinning around in a circle thanks to the motor on the plane. The length of the string that is connected to the plane is 0.635 meters, the radius of the circle the plane is traveling in is 0.54 meters, and the angle of the rope where it connects to the ceiling is 58.25 degrees (sin^-1 (r/L)=angle of string). Find the seconds per each revolution of the plane (T).

Answer 1

1.87 s

Step-by-step explanation:

There are two forces on the plane:

Weight force mg pulling down,

and tension force T pulling along the string.

Sum of forces in the y direction:

∑F = ma

T sin θ − mg = 0

T = mg / sin θ

Sum of forces in the centripetal direction:

∑F = ma

T cos θ = m v² / r

mg / tan θ = m v² / r

g / tan θ = v² / r

v² = gr / tan θ

Plug in values:

v² = (9.8 m/s²) (0.54 m) / tan 58.25°

v = 1.81 m/s

The period is equal to the circumference divided by the speed.

T = 2πr / v

T = 2π (0.54 m) / (1.81 m/s)

T = 1.87 s