Question

A block weighing W is resting on a plane inclined at q to the horizontal. The
coefficient of friction is m. The force P required to pull it up the plane is
aW
(a) W sin q - mW cos q
O
(b) W sin q + m W cos q
0 q
(c) W cos q- mW sin q
0 (d) W cos q + m W sin q​

Answer 1

Answer:

In the limiting case contact force F is inclined at λ to the normal. Only three forces act on the block.

Applying Lami's theorem, we get:

sin(180

∘

−λ)

P

=

sin(90

∘

−θ+λ)

W

sin(90

∘

+θ)

F

or

sinλ

P

=

cos(θ−λ)

w

or P=

cos(θ−λ)

W

P will be least when cos(θ−λ) is greatest because W and λ are constant.

i.e., when cos(θ−)=1 and θλ=0

∘

or θ=λ