- #1
rpthomps
- 182
- 19
Homework Statement
A uniform sphere of radius R is supported by a rope attached to a vertical wall,as shown in the figure. The point where the rope is attached to the sphere is located so a continuation of the tope would intersect a horizontal line through the sphere’s centre a distance R/2 beyond the centre, as shown. What is the smallest possible value for the coefficient of friction between wall and sphere.
Homework Equations
##T_x=F_N\\\\F_f+T_y+Mg\\\\\Sigma\tau=0=\frac{1}{2}RMg-RF_f\\\\tan30^o=\frac{T_x}{T_y}\\\\F_f=\mu F_N##
The Attempt at a Solution
##\frac { 1 }{ 2 } RMg=RF_{ f }\\ \\ \frac { 1 }{ 2 } Mg=\mu F_{ N }\\ \\ \\ \frac { 1 }{ 2 } Mg=\mu T_x\\ \\ ##
equation 1
##F_f+\frac{T_x}{tan30^o}=Mg\\\\\mu F_N+\frac{T_x}{tan30^o}=Mg\\\\\mu T_x+\frac{T_x}{tan30^o}=Mg\\\\##
equation 2Solve equation 1 for Tx and substitute into equation 2.##\mu=\frac{1}{tan30^o}=1.73…##Back of the book says 0.87