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.