- #1

jonjacson

- 453

- 38

Hi to everybody

(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.

Newton laws and basic trigonometric relationships.

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√(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

## 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√(r

^{2}-s^{2}))/rDoes 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