Vertical Circles: mg vs Resultant Force

[binbagsss]

At the top of a circle, does the direction of the contact force depend on whether or not mg is > than or < than the resultant force?

So when mg is < than the resultant force, mg is acting downward but there is a greater force than this toward the centre, so to compensate for this the contact force must also be acting downward, so F=mg+R ( where R is the contact force ).

And when mg is > than the resulstant force, the contact force must be acting upward to provide the smaller centripetal force, so F= mg -R.

But at the bottom F always = R-mg.

However I am confused with vertical circles where e.g. a stone is being whirled. The formula for the top of the circle is always given as F = T + mg, where T is the tension. So T always acts downwards? I don't really understand this...thanks !

 

[rock.freak667]

However I am confused with vertical circles where e.g. a stone is being whirled. The formula for the top of the circle is always given as F = T + mg, where T is the tension. So T always acts downwards? I don't really understand this...thanks !

The tension will always act towards the center of rotation while the weight will always act vertically downwards.

So at the top of the circle, the tension is acting down and the weight is acting down. The resultant force towards the center of the circle is F= T+mg.

At the bottom: The tension acts up towards the center of the circle and the weight acts down (away from the center of the circle). The resultant force towards the center of the circle is F=T-mg.

 

[binbagsss]

The tension will always act towards the center of rotation while the weight will always act vertically downwards.

So at the top of the circle, the tension is acting down and the weight is acting down. The resultant force towards the center of the circle is F= T+mg.

At the bottom: The tension acts up towards the center of the circle and the weight acts down (away from the center of the circle). The resultant force towards the center of the circle is F=T-mg.

yehh, but why does tension always act towards the centerr ? :)

 

[ehild]

A string can only pull. If it is a rod, the tension can act in both directions.

ehild

 

[rwisz]

I would like to clarify that the direction of the contact force at the top of a vertical circle does not depend on whether mg is greater or less than the resultant force. The contact force, also known as the normal force, is a reaction force that is always perpendicular to the surface of contact. In the case of a vertical circle, the normal force will always be directed towards the center of the circle, regardless of the value of mg or the resultant force.

At the top of the circle, the net force acting on the object is equal to the centripetal force, which is the sum of the tension force (T) and the weight force (mg). The tension force is acting downwards because it is pulling the object towards the center of the circle, while the weight force is always directed downwards due to gravity. Therefore, the normal force must also be directed downwards to balance out the net force and keep the object moving in a circular path.

At the bottom of the circle, the net force is still equal to the centripetal force, but the direction of the normal force changes. This is because the tension force is now acting upwards, while the weight force is still acting downwards. Therefore, the normal force must act upwards to balance out the net force and maintain the circular motion.

In summary, the direction of the contact force at the top and bottom of a vertical circle is determined by the direction of the net force, which is dependent on the tension and weight forces. The value of mg or the resultant force does not affect the direction of the contact force.