why should centipetal force and weight be equal?

Question

from lab involving spinning a stopper on string with varying dangling mass...

briefly explain the relationship between the centripetal force an the amount of hanging weight. why should they be equal?

Answer 1

when u use the word "centripetal force"...it means..it is a force needed 2 move the object in a circular direction with uniform speed and directed towards the center...to make any object move...,,,the force must be equal to its weight..then only the object would move!!!!!!!!

Answer 2

f = ma = the net forces (f) acting on a body of mass (m) to give it acceleration (a).

If all the forces acting on a body are C and W (centripetal and weight) and that body is not moving (acceleration a = 0), f = ma = 0 = C + W; so that C = -W, the centripetal force must be equal and opposite to the weight. Otherwise, there would be a nonzero net force and there would be acceleration.

For example, assume C > -W so that C + W > 0; then f = ma = C + W > 0; in which case, ma > 0 and since there is no such thing as negative mass a > 0 also. That is, the acceleration would be upward away from the force of the weight.

Bottom line, if a body is not accelerating (stopped or uniform velocity) the sum of ALL forces acting on it must be zero so that f = ma = 0. And that's why centripetal force and weight are "equal" in your case.

Answer 3

centripital force keeps the object from dangling so it goes in a smooth circle because it pulls it towards the center of the string. If the weight of the object is larger than the centripital force then the object will just go down because the tension in the string (centripital force) is not enough to overcome the force created by gravity.
Try spinning a 1 kilo object it requires a lot of centripital force to stay in the circle because gravity wants to pull it down and centripital force wants it to go towards the center.

W = mg <== O------------- ==> Ac = v^2/r (i think)
when the two are equal the net force equals 0.
Remember also that the velocity of centripital force is perpendicular to the circle so thats why it moves in a circle.

Answer 4

The Centripetal force will be the tension force in the string, which will be equal in magnitude to m*g (weight), as at the bottom, the object will be in equilibrium, and therefore the two vertical forces (weight and gravity) will cancel.