Centripetal Motion along the horizontal with an angle

In summary, a 0.20 kg stone attached to a 0.8 m long string is rotated in a horizontal plane. The string makes an angle of 25° with the horizontal. The stone moves at a speed of 4.2075 m/s.
  • #1
mpmor1
8
0

Homework Statement



A 0.20 kg stone attached to a 0.8 m long string is rotated in a horizontal plane. The string makes an angle of 25° with the horizontal. Determine the speed of the stone.

Homework Equations



V= √(Fr/m)

The Attempt at a Solution



find the vertical component, call it y, then say F= y/sin(θ)
 
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  • #2
What forces act on the stone? (Hint: Two forces act.) Consider the vertical and horizontal force components and apply Newton's 2nd law to each.
 
  • #3
if the total force is broken into its horizontal and vertical components, can its force of weight (1.962N) be treated as the vertical component?
 
  • #4
mpmor1 said:
if the total force is broken into its horizontal and vertical components, can its force of weight (1.962N) be treated as the vertical component?
What do you mean by 'total force'? Realize that in the formula in your first post, that "F" has to be the centripetal force.

I think that's a confusing way to go about it. Better to think of centripetal acceleration = v2/r.

Did you draw yourself a free body diagram? What forces act? The weight is one of the forces.
 
  • #5
The two forces acting on the stone are its weight, pointing straight down, and the unknown centripetal force which can be seen as the tension in the string
 
  • #6
mpmor1 said:
The two forces acting on the stone are its weight, pointing straight down, and the unknown centripetal force which can be seen as the tension in the string
Almost.

The two forces acting on the stone are its weight and the tension in the string. The horizontal component of those forces must produce the centripetal acceleration. (Centripetal force is just the name we give to the net force in the centripetal direction. It's not a separate force. It never appears on a free body diagram.)
 
  • #7
So if the horizontal component is the centripetal Force, that being 4.2075N, then this can simply be plugged into the equation V= sqrt(Fr/m)?
 
  • #8
mpmor1 said:
So if the horizontal component is the centripetal Force, that being 4.2075N,
How did you solve for that component? (But you're right.)
then this can simply be plugged into the equation V= sqrt(Fr/m)?
Yep. (But there's a slightly easier way.)
 
Last edited:
  • #9
If the mass of the stone is .2kg then the weight is 1.962N; this would make the horizontal component equal to that divided by the tangent of the angle, 25.
 
  • #10
I was editing my response while you were writing your post.
 
  • #11
That doesn't yield the correct answer online
 
  • #12
mpmor1 said:
That doesn't yield the correct answer online
What did you use for r?
 
  • #13
.8m, the length of the string
 
  • #14
mpmor1 said:
.8m, the length of the string
There's your problem. r stands for the radius of the circular path, which is not the length of the string. Use a little trig to figure out r.
 
  • #15
thanks
 

1. What is centripetal motion along the horizontal with an angle?

Centripetal motion along the horizontal with an angle is a type of circular motion where an object moves along a horizontal path while its velocity is constantly changing in direction towards the center of the circle.

2. What causes an object to experience centripetal motion along the horizontal with an angle?

An object experiences centripetal motion along the horizontal with an angle when it is subjected to a force directed towards the center of the circle.

3. How is the magnitude of centripetal force calculated for an object in this type of motion?

The magnitude of the centripetal force can be calculated using the formula F = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circle.

4. Can an object experience centripetal motion along the horizontal with an angle without a force acting on it?

No, an object cannot experience centripetal motion along the horizontal with an angle without a force acting on it. Without a force, an object will continue to move in a straight line at a constant velocity.

5. How does the angle affect the centripetal force in this type of motion?

The angle at which the object is moving will affect the direction of the centripetal force. As the angle increases, the force required to keep the object moving in a circular path also increases.

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