- #1
Bruneleski
- 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]
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.[/B]