Question

I'm looking for help factoring gravity into centripetal force equations, I know how to do ones without gravity just fine.

Answer 1

Step 1;

Given,

The mass of the person, m=57.0 kg

The radius of the track, R=42.7 m

The normal force acting on the person, N=995 N

Step 2:

The centripetal force required for the person is provided by the sum of the difference in the normal force and the weight of the person.

Thus the centripetal force on the person is given by,

`F_c=(mv^2)/(R)=N-mg`

Where v is the speed with which the car and the person are moving and g is the acceleration due to gravity.

On rearranging the above equation,

`v=\sqrt[]{(R)/(m)(N-mg)}`

Step 3:

On substituting the known values in the above equation,

`\begin{gathered} v=\sqrt[]{(42.7)/(57.0)*(995-57.0*9.8)} \\ =18.08\text{ m/s} \end{gathered}`

Thus the velocity of the car is 18.08 m/s