Question

A block rests on a smooth inclined plane making an angle of 30 degree with the horizontal. the coefficient of static friction between the block and the plane is 0.8 . if the frictional force of the block is 10N , what is the mass of the block?

Answer 1

f=mgsin30
or 10=m*10*0.5
or m=2 kg

Answer 2

f=0.8N
f=0.8*mgcos30
or, \(\huge{10=0.8*m*10*\frac{ \sqrt{3} }{ 2 }}\)
or \(\huge{m=\frac{ 10 }{ 4\sqrt{3} }}\)
or m~1.44 kg

Answer 3

I got two answers !

Answer 4

isnt mg sin theta the force without friction ?

Answer 5

its the component of mg parallel to the inclined plane...

Answer 6

if memory serves;

mg sin(30) is the force being applied in the direction of motion ... which needs to overcome the force of the static friction stuff in order to move.

once it starts moving, there is a kinetic friction involved.

Answer 7

so when it is about to move...(just going to move)
then mgsin30 = f

Answer 8

the force to start moving it: mg sin(30) will be greater (or equal?) to the .8 mg cos(30)

yes

Answer 9

maximum frictional force = friction static coefficient * normal force
it isnt said that this frictional force is maximum. It would be maximum if the mass were 1,44, so i think Your first solution is correct because newtons second law must hold.

Answer 10

Your first answer is the right one.

The second answer makes the false assumption that f = 0.8 N, as Fifciol rightly explained.

Answer 11

thank u sir and all you guys...!:)

Answer 12

1. Weight ( mg, down)
2. Normal force (N, diagonally perpendicular to slope)
3. Friction (F = 10 Newtons, pointing upslope)

The vector components parallel to the slope are:
1. -(mg)sinθ (negative because it points downslope)
2. 0 (Normal force has no slope-parallel component)
3. +F

Apply Newton's 2nd Law:

Fnet_parallel = m(a_parallel)
-(mg)sinθ + 0 + F= m(0)
-(mg)sinθ + F = 0

Solve for "m":

m = F / (g*sinθ)

Substitute 10 Newtons for "F", and 30 degrees for "θ", then push the little buttons on your calculator. (Note the coefficient of friction is irrelevant.)

so your first answer is the correct ..

Answer 13

thanks...:)

Answer 14

Welcome ,, good luck :)

Answer 15

The coefficient of friction is not used in the final answer, but you can check it it greater that tan 30°, otherwise the block would not be at rest.