If you're only given the radius of a circle, how do you find the centripetal force? The hint is what is the centripetal acceleration at the top of the circle?
You cant, unless you know something about the velocity. If the velocity is just sufficent to keep the mass in a vertical circle, then at the top mg= mv^2/r
To find the centripetal force of a circle, you need to have additional information besides just the radius. Specifically, you need to know either the velocity or the mass of the object moving in the circle. The centripetal force is given by the equation Fc = (mv^2)/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circle.
However, in the given scenario where you only have the radius of the circle and a hint about the centripetal acceleration at the top of the circle, it is possible to make an assumption about the velocity. The hint suggests that the velocity at the top of the circle is just sufficient to keep the mass in a vertical circle. In this case, at the top of the circle, the force of gravity (mg) is equal to the centripetal force (mv^2/r) acting towards the center of the circle.
Therefore, if you are given the radius of the circle and the mass of the object, you can equate mg to mv^2/r and solve for the velocity (v). Once you have the velocity, you can then calculate the centripetal force using the equation Fc = (mv^2)/r.
It's important to note that without any information about the mass or the velocity, it is not possible to determine the value of the centripetal force solely based on the radius of the circle.