# What is The force a body exerts on a vertical circular track?

I am trying to calculate the force a body exerts on a vertical circular track with no friction at its highest point I know the centripetal force at that point is mg and the given data is the velocity the mass of the body the gravitational constant and the radius of the track what do I do now?

• "I know the centripetal force at that point is mg" Are you sure that the only centripetal force is $mg$? – lucas May 29 '16 at 20:34
• The formula for the centripetal force is F=(mv^2)/r and the speed given is the square root of g*r from that I arrived at mg – Lendion May 29 '16 at 20:38
• Let me exapnd of @lucas's comment: it is not, in general, true that the centripetal acceleration at the top of the loop is $g$. That is: you can't take this as a given and have to prove it for any particular case you wish to use it in. – dmckee May 29 '16 at 21:51
• It is a particular teoretical case where the speed at the highest point is given to be the square root of m*g – Lendion May 30 '16 at 5:58

• Newton's law is not exactly $F=ma$ but rather $\sum F=ma$. The $\sum F$ must include all forces in the vertical-direction. You mention gravity $w=mg$, yes, but as @lucas refers to in the comments above, this is not the only force in the vertical direction. – Steeven May 29 '16 at 21:49