Kayla, a fitness trainer, develops a new exercise. The exercise involves using a rope to pull a crate of mass \( M=45.0 \mathrm{~kg} \) along a carpeted track. Using her physics expertise, Kayla determines that the coefficients of kinetic and static friction between the crate and the carpet are \( \mu_{\mathrm{k}}=0.470 \) and \( \mu_{\mathrm{s}}=0.730 \), respectively.
Kayla uses one of her employees, Ramon, to test the exercise.
Use \( \mathrm{g}=9.80 \mathrm{~m} / \mathrm{s}^{2} \) for the gravitational acceleration.
If the rope makes an angle of \( \theta=29.0^{\circ} \) with the floor, what is the minimum force \( F_{\min } \) that Ramon must apply to set the crate in motion?
\[
F_{\min }=
\]
N