What Is the Role of Static Friction on an Inclined Plane?

[r3dxP]

7. A block of mass m is at rest on a plane inclined at an angle of 30o with the horizontal as shown below. Which of the following statements about the force of static friction is necessarily true??A. s greater than/equal to g?B. s equal to tan ?C. s less than/equal to tan ?D. s greater than/equal to tan
i don't know how to do this.. i think the static friction is equal to tan(angle) , so would it be B ?


i tried to do #3, but not sure if i did it right, and i have no idea how to do #4, pls help~
3. In the figure below, the block slides down the plane. What are
A. the magnitude of the blocks acceleration

g*sin(30degrees) = 4.9 m/s^2

B. the magnitude of the normal force on the block from the inclined surface?

Fn = ?
Fn = m*a*cos(degrees) = m*g*cos(30degrees) = m * 8.5m/s^2
thus, a = 8.5 m/s^2

4. In the figure below, a 60.0 N force F, directed upward, is applied to the block.
A. What are the magnitude and direction of the blocks acceleration?

B. What is the magnitude of the normal force on the block from the inclined surface?
C. What must the magnitude of the applied force be if the block is to be stationary?

 

[hotvette]

kind of hard to help w/o the figures.

 

[r3dxP]

ok this question can be solved by drawing it out rather than looking at a drawn diagram..
12. In an amusement park ride, riders stand with their backs against the wall of a spinning vertical cylinder. The floor falls away and the riders are held up by friction. If the radius of the cylinder is 4 m, find the minimum number of revolutions per minute necessary when the coefficient of static friction between a rider and the wall is 0.4??

 

[mukundpa]

The normal reaction of the wall provides required centripetal force $$m \omega^2 R$$ hence the upward friction force balancing the weight of the person hence $$\mu m \omega^2 R = mg$$ will give required angular velocity $$\omega$$.