Question

The mass of a roller-coaster car, including its passengers, is $500kg$. Its speed at the bottom of the track in above figure is $19m/s$. The radius of this section of the track is $r_1=25m$. Find the force that a seat in the roller-coaster car exerts on a $50kg$ passenger at the lowest point.

Answer 1

The free-body diagram of the passenger is shown in below figure. From Newton’s second law
$\sum F_y=m{a}_y$
$n-mg=\frac{m{v}^2}{r}$
which gives
$n=mg+\frac{m{v}^2}{r}$
$=\left(50kg\right)\left(9.80m/s^2\right)+\frac{\left(50.0kg\right)(19m/s{)}^2}{25m}$
$=1.2\times {10}^{3}N$