Loop related to Circular motion

In summary, a skate boarder must have an initial speed that is high enough to match the centripetal acceleration and neutralize gravity in order to successfully complete a loop without friction. This can be calculated using conservation of energy and the equation vf2 / r = g. Another proposed formula, v2 = Tension + mg, may not be applicable in this situation.
  • #1
Kikki:)
17
0

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.
 
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  • #2
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.
 
  • #3
Hi Kikki:) Welcome to PF! :smile:

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:
vf2 / r.

To achieve that he should have an initial speed dictated by conservation of energy, that is:
vi2 / 2 = vf2 / 2 + g h
 
  • #4
I like Serena said:
Hi Kikki:) Welcome to PF! :smile:

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:
vf2 / r.

To achieve that he should have an initial speed dictated by conservation of energy, that is:
vi2 / 2 = vf2 / 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
 
  • #5
Kikki:) said:
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! :smile:

He needs to have a speed high enough to neutralize gravity, that is:
vf2 / r = g
Kikki:) said:
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? :confused:

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... :wink:
 

1. What is a loop in circular motion?

A loop in circular motion refers to a complete rotation of an object along a circular path. This means that the object has traveled a full 360 degrees and has returned to its initial position.

2. What causes an object to loop in circular motion?

An object loops in circular motion due to the balance between its velocity and centripetal force. The velocity of the object determines the direction of its motion, while the centripetal force acts as the inward force that keeps the object moving in a circular path.

3. Can an object loop in circular motion without a centripetal force?

No, an object cannot loop in circular motion without a centripetal force. The centripetal force is necessary to maintain the object's circular path and prevent it from flying off in a straight line.

4. What is the difference between a loop and a revolution in circular motion?

A loop refers to a complete rotation around a circular path, while a revolution refers to a single full rotation around a fixed point. In other words, a loop is a type of revolution in which the object returns to its starting point.

5. How can you calculate the speed of an object in a circular loop?

The speed of an object in a circular loop can be calculated using the formula v = 2πr/T, where v is the speed, π is pi (approximately 3.14), r is the radius of the circular path, and T is the time taken for one full rotation.

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