Fnet>10.5What causes the block to not initially move up or down the incline?

[rash92]

Homework Statement

A block of mass 30 kg rests 12 m from the bottom
of an inclined plane that is at an angle of 60 to the horizontal. It is connected by a rope of negligible mass via a frictionless pulley to a bucket of mass 5 kg of water, hanging vertically as shown in Fig. Q3. The static and dynamic coefficients of friction between the block and the plane are 0.7 and 0.4, respectively. Water leaks from the bucket at a constant rate of 20 g s-1.

Show that the block will not initially move up or down the incline

if the above is unclear, it is question 3 b on past paper that is attached.

Homework Equations

sohcahtoa equations
Friction = mu*R
R = mgcos60
F = ma
mu(static max) = .7
mu(dynamic) = .4

The Attempt at a Solution

after doing a free body diagram trying to look at whether the block can go down, i got the net force on the block is:
Fnet = component of gravity - tension from bucket - friction
Fnet = Mblock*gsin60 - Mbucket*gsin60 - Mblock*mu*gcos60
= 30gsin60 - 5gson60 - 5*.7*gcos60
= 121.3 N

the question is saying that there should be no net positive force (since the static friction should go up and cancel it, but using max static friction I'm still getting a net force).

 

[azizlwl]

Find the net force of mgsinθ and tension of the bucket.
If this is less than μ_smgCosθ then it will not move.
Since no motion net force=static friction

 

[rash92]

the tension is in the opposite direction of mgsinθ though, tension is in the same direction as the friction would be.

 

[azizlwl]

Friction will oppose any motion.
We need net force to move an object.
For static friction, it is equal to the force apply(object not moving).
If you push lightly on an object on a rough surface and its not moving, the force you apply equal to friction. In this case friction is not equal to μ_staticmg but equal to force applied.
When the force apply =μ_staticmg then it will start to move. Since the maximum static friction is reached.
http://en.wikipedia.org/wiki/Friction#Static_friction

 

[rash92]

i know that, but it still wasn't working.

EDIT: turns out the question in the paper was wrong, it DOES move.

 

[azizlwl]

Yes you are right

|30gSin60°-5g|>μ30gCos60°
|21|>10.5