Loop related to Circular motion

[Kikki:)]

Homework Statement

The radius is 7ft, the diameter is 14ft, the person is 181lb and is 6ft 1in.

How fast does he have to start the loop to be successful all the way around?
How high does he have to start?
Don't need to apply Friction.

Homework Equations

Cetripetal Force? Flo Diagram?

The Attempt at a Solution

I'm not getting how to start or find it. I know possibly kinematics is involved with it.

 

[Kikki:)]

I also forgot to mention that it is a skate boarder going down a ramp and into a big loop, it was off of jackass, out teacher is made this equation from it by just estimating it. I'm mainly wanting to learn how to do the problems. :] So would you try to find the circumference first? So would the final speed be 0 ? I know that the gravity force is 9.8 m/s/s. A possible equation from kinematics would be final velocity= initial velocity + acceleration x time. But the problem is I would need to know the time.

 

[I like Serena]

Hi Kikki:) Welcome to PF!

I'd recommend using conservation of energy combined with the required centripetal acceleration to stay in a circular trajectory.

At the top the center of mass of the skater should have a speed high enough to match the centripetal acceleration, that is:
v_f² / r.

To achieve that he should have an initial speed dictated by conservation of energy, that is:
v_i² / 2 = v_f² / 2 + g h

 

[Kikki:)]

Hi Kikki:) Welcome to PF!

I'd recommend using conservation of energy combined with the required centripetal acceleration to stay in a circular trajectory.

At the top the center of mass of the skater should have a speed high enough to match the centripetal acceleration, that is:
v_f² / r.

To achieve that he should have an initial speed dictated by conservation of energy, that is:
v_i² / 2 = v_f² / 2 + g h

But how do you exactly figure out the final velocity because I tried it as having it as zero. I also came up with a formula too that I think could work also related to yours.

v²=Tension + mg

 

[I like Serena]

But how do you exactly figure out the final velocity because I tried it as having it as zero.

If the final velocity (at the top) would be zero, the skater wouldn't be going forward anymore, and fall straight down. Ouch!

He needs to have a speed high enough to neutralize gravity, that is:
v_f² / r = g

I also came up with a formula too that I think could work also related to yours.

v²=Tension + mg

Huh? Don't know that one?

What is "Tension"?
The units don't match, that is, v² is not a force like the others...

Apparently this is supposed to be a forces sum, but consider when it would be applicable and what the directions / signs should be...