Question

A small remote-control car with a mass of 1.65 kg moves at a constant speed of v = 12.0 m/s in a vertical circle inside a hollow metal cylinder that has a radius of 5.00 m. What is the magnitude of the normal force (in N) exerted on the car by the walls of the cylinder at point A (at the bottom of the vertical circle)?

Answer 1

Answer:

$N=63.69N$

Explanation:

The normal force exerted on the car by the walls of the cylinder at the bottom of the vertical circle will be such that when substracted to the weight it must give the centripetal force, since at that point on the vertical $F_{cp}=N-W=N-mg$

We also know that the equation for the centripetal force is:

$F_{cp}=ma_{cp}=\frac{mv^2}{r}$

Mixing both equations we get:

$N-mg=\frac{mv^2}{r}$

$N=mg+\frac{mv^2}{r}$

Which for our values means:

$N=(1.65Kg)(9.8m/s^2)+\frac{(1.65Kg)(12m/s)^2}{(5m)}=63.69N$