Problem

A uniform box is placed in a position along the

inclined plane which makes an angle $$ from

the horizontal. Coefficient of static friction

$=0\mathrm{.}45.$

$(1)$ Determine the largest angle $$ for which

the uniform box can be in equilibrium.

a$)16\mathrm{.}38$

c$)20\mathrm{.}57$

b$)24\mathrm{.}23$

d$)32\mathrm{.}35$

$(2)$ If $=32,$ determine the greatest height

$"h"$ parallel to the $1\mathrm{.}2m.$ height of box at

which a force $P$ parallel to the inclined

maybe applied so that the block will slide

up the incline without tipping over.

a$)0\mathrm{.}3157m.$

c$)0\mathrm{.}5814m.$

b$)0\mathrm{.}7859m.$

d$)0\mathrm{.}1563m.$

$(3)$ If the force $P$ is applied at a height of

$h=0\mathrm{.}58m.,$ determine the force $P$ to

cause motion to impend. Assume weight

of block is $8kN.$

a$)7\mathrm{.}30kN$

c$)5\mathrm{.}57kN$

b$)2\mathrm{.}26kN$

d$)9\mathrm{.}25kN$