A girl sits on a tire that is attached to an overhanging

tree limb by a rope 2.13 m in length.
The girl’s father pushes her with a tangential
speed of 2.92 m/s. Besides the force opposing
the girl’s weight, the magnitude of the force
that maintains her circular motion is 81.3 N.
What is the girl’s mass?
Answer in units of kg.

F = m v^2/R

81.3 = m (2.92)^2 / 2.13

To find the girl's mass, we can use the centripetal force equation:

F = (m * v^2) / r

Where:
F = force maintaining circular motion (81.3 N)
m = mass of the girl (unknown)
v = tangential speed (2.92 m/s)
r = radius of the circular motion (length of the rope = 2.13 m)

Rearranging the equation, we can solve for the girl's mass:

m = (F * r) / v^2

Substituting the given values:

m = (81.3 N * 2.13 m) / (2.92 m/s)^2

m ≈ 39.676 kg

Therefore, the girl's mass is approximately 39.676 kg.

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