Calculate the force on a circular surface

In summary, the homework statement has a problem with the force applied and the equations to calculate it.
  • #1
jonjacson
453
38
Hi to everybody

Homework Statement



(The attachment has an image with this problem)

A small probe P is gently forced against the circular surface with a vertical force F as shown. Determine the n- and t-components of this force as functions of the horizontal position s.

Homework Equations



Newton laws and basic trigonometric relationships.

The Attempt at a Solution



Well I show in the attachment my reasoning, the force F is applied at the contact point C, I have represented the direction in which this force acts (vertical line). I need to find the proyections of F to the n and t axis, to calculate Fn and Ft in red.

Well I think that the angle between the vertical line and the line connecting the center O and the point C is the same angle between F and Fn, in the picture they are called A. I simply write:

Fn= F cos(A)
Ft= F sen(A)

And I can calculate A as:

A=arcsen(s/r)

But I have seen the answers provided in the book and they are:

Ft=Fs/r

and

Fn= -(F√(r2-s2))/r

Does anybody know what is Fs?

And I have no idea where the equation for Fn comes from.

Why are my answers so different to the ones in the book?

Thank you
 

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  • #2
"Fs" is F*s, not Fs. Looks like they are avoiding using sin, cos in the answer.
 
  • #3
jonjacson said:
Fn= F cos(A)
Ft= F sen(A)

And I can calculate A as:

A=arcsen(s/r)

Looks good. (The sine function is generally written sin rather than sen.) From A=arcsin(s/r) you get sin(A) = s/r. Try substituting this expression for sin(A) into your expression Ft= F sin(A) and compare to answer in book.
 
  • #4
jonjacson said:
And I have no idea where the equation for Fn comes from.
How would you write cos(A) in terms of s and r?
 
  • #5
TSny said:
Looks good. (The sine function is generally written sin rather than sen.) From A=arcsin(s/r) you get sin(A) = s/r. Try substituting this expression for sin(A) into your expression Ft= F sin(A) and compare to answer in book.

lewando said:
"Fs" is F*s, not Fs. Looks like they are avoiding using sin, cos in the answer.

Yes you are right, thank you very much.

The sinus is simply s/r and I get the Ft.

For the Fn it´s the same, they avoid to use the cos, to calculate the other leg of the triangle I use the pythagorean theorem r2=s2+y2 where I called y the other leg of the triangle. So the cosinus is exactly the answer in the book.

Thank you very much to both of you, I have more doubts with problems in this book, hope to see you in the other threads.:biggrin:
 

FAQ: Calculate the force on a circular surface

1. What is the formula for calculating the force on a circular surface?

The formula for calculating the force on a circular surface is F = P x A, where F is the force, P is the pressure, and A is the area of the circular surface.

2. How do you determine the pressure acting on the circular surface?

To determine the pressure acting on the circular surface, you need to know the force applied to the surface and the area of the surface. You can then use the formula P = F/A to calculate the pressure.

3. Can you use this formula to calculate the force on any circular surface?

Yes, this formula can be used to calculate the force on any circular surface as long as you know the pressure and area of the surface. However, it is important to note that the surface must be a perfect circle for this formula to be accurate.

4. How does the force on a circular surface differ from the force on a flat surface?

The force on a circular surface is calculated using the pressure and area of the surface, while the force on a flat surface is calculated using the pressure and the length and width of the surface. Additionally, the distribution of force on a circular surface is uniform, while on a flat surface it can vary depending on the shape and placement of the applied force.

5. What are some real-life applications of calculating the force on a circular surface?

Calculating the force on a circular surface is important in various engineering and design applications, such as determining the force on a car tire, calculating the pressure on a diving board, or designing a hydraulic press. It is also useful in understanding the effects of fluid pressure on circular objects, such as submarine hulls or propellers.

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