Help with Laws of Motion Problem

[physixguru]

Homework Statement

An insect crawls very slowly on a hemi-spherical shell..
The coeff. of friction between insect and surface of sphere is 1/3.
The line joining the centre of the shell to the insect makes an angle of @ with the vertical.

THE MAX VALUE OF @ IS DEFINED BY...?

a)cosec@=3
b)tan@=3
c)cot@=3
d)sec@=3

Help will be higly appreciated>><<

 

[dynamicsolo]

Homework Statement

An insect crawls very slowly on a hemi-spherical shell..
The coeff. of friction between insect and surface of sphere is 1/3.

The thing to consider is this. What angle would a flat surface make to the horizontal before an object on it would just start to slip, if the coefficient of friction between that object and the surface were
1/3? Now consider a small flat surface that is tangent to the surface of the hemisphere. Where on the shell would the tilt of that surface to the horizontal have that value you found? For the imaginary line from the center of the shell to that tangent point on the shell's surface, what angle to the vertical does that line make? (A little drawing would be helpful here.)

 

[physixguru]

Sir i think the concept to be used here is the same as that of angle of repose in an inclined plane...i.e. the maximum value of inclination that prevents the object to slip...

am i correct with the thought application?

 

[physixguru]

thanks a lot sir...

your concept of placing a horizontal plane was really helpful...

i assumed the plane to be a banked road for the insect..and then since the ques says that the insect moves very slowly..then i am sure it does not possesses the max velocity..
for a car on a banked rd and whose v is less than v[max]..the car can be parked only if
tan@<=coeff. of friction.
similarly the case with insect on the hemispherical shell...

applying the rule,,we get...

tan@<=1/3
solving we get..cot@<=3

hence max angle is defined by...cot@=3.

THANKS A LOT AGAIN...

 

[dynamicsolo]

..the car can be parked only if
tan@<=coeff. of friction.
similarly the case with insect on the hemispherical shell...

A velocity is not really important to the problem. As with the car on the banked road, the issue is with the amount of static friction. The insect would not even be able to stay in place if it were further down on the shell.

applying the rule,,we get...

tan@<=1/3
solving we get..cot@<=3

hence max angle is defined by...cot@=3.

I agree. :-) (The angle that the imaginary tangent plane makes to the horizontal is the same as the angle the line from the center of the shell to the tangent point makes with the vertical.)