- #1

- 22

- 1

## Homework Statement

Body of mass m is being pulled by a string so that it moves horizontally at constant speed.

Friction coefficient between surface and body is u.Find an angle (alpha) between a string and horizontal surface for which tension in string is minimal and find that tension.

## Homework Equations

weight w=mg ; n=normal force

friction force=f=un

acceleration due x-axis=0

tension T

## The Attempt at a Solution

[tex]

\sum F_y=Tsin(\alpha)+n+(-w)=0; \\

T=\frac{(mg-n)}{sin(\alpha)} \\

\sum F_x=Tcos(\alpha)+(-f)=0 \\

\sum F_x=Tcos(\alpha)+(-un)=0; \: Tcos\alpha=un ; \\

T=\frac{umg}{cos\alpha} \\

\frac{(mg-n)}{sin(\alpha)}=\frac{umg}{cos\alpha} \\

tan\alpha=\frac{mg-n}{umg}

[/tex]

**[/B]**

Now I'm not sure what to do next.I need to find minimal angle so derivative of the last expression should be zerr should I differentiate arctan?I'm confused.

Now I'm not sure what to do next.I need to find minimal angle so derivative of the last expression should be zerr should I differentiate arctan?I'm confused.