Uniform Circular Motion: Tension Force at Top of Circle

[daisy7777]

Homework Statement

A 500.0 g mass is whirling around a vertical circle (it lies in a plane perpendicular to the ground) with a radius of 70.0 cm. If the mass is moving with a frequency of 0.800 Hz, calculate the tension force at the top of the circle.

Relevant Equations

ac = vpi^2rf^2
Fc = m*ac
Fc = Fg - Ft

I calculated the acceleration which is 0.804m/s^2. From there I calculated the centripetal force which is 0.402N. I think my lack of answer is due to my lack of understanding of the concept of what the centripetal force is at the top of the circle. Would it not be Fc = Fg - Ft as the ball wouldn't be dropping? Or would it be Fc = Fg + Ft because the tension force is moving in the same direction as gravity? If that's the case, when I solve for Ft, I get -4.50. But this isn't the answer for the question.

 

[kuruman]

Draw and post a free body diagram of the mass at the top of the trajectory. The we can discuss what it says in terms of Newton's second law. Remember, that "centripetal" is just another name for "having direction towards the center." For example, at the top of the trajectory, gravity is centripetal. The only other force acting on the mass is tension. In what direction is that at the top of the trajectory. Of course the vector sum of the tension and gravity is the net force acting on the mass. What is the direction of that? Is it centripetal or not?

 

[haruspex]

If that's the case, when I solve for Ft, I get -4.50

Please post your steps. I get a different result if I pretend the speed of the mass is constant. In practice, of course, it will be less at the top, but that makes it a tough problem.

 

[daisy7777]

Draw and post a free body diagram of the mass at the top of the trajectory. The we can discuss what it says in terms of Newton's second law. Remember, that "centripetal" is just another name for "having direction towards the center." For example, at the top of the trajectory, gravity is centripetal. The only other force acting on the mass is tension. In what direction is that at the top of the trajectory. Of course the vector sum of the tension and gravity is the net force acting on the mass. What is the direction of that? Is it centripetal or not?

Would this be correct then? I have the centripetal force as the force of gravity and the force of tension b/c I think they'd both be in the same dir. at the top of the circle.

 

[haruspex]

View attachment 341812
Would this be correct then? I have the centripetal force as the force of gravity and the force of tension b/c I think they'd both be in the same dir. at the top of the circle.

The numbers look right, shame about the missing units for the force.
Round it to 3 sig figs to match the given data.