a partical of mass m rest on a horizontal floor with which it has a coefficent of a static friction u for the block to just movie 1, the menimum five has applied2, at the a angle thita with the horizontalare
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Answer:
Plz give us the formula to calculate the static friction too....
Explanation:
Sorry
Answer:
11th
Physics
Laws of Motion
Motion Along a Rough Inclined Plane
A block of mass m rests on ...
PHYSICS
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Asked on December 26, 2019 by
Amoira Ahsan
A block of mass m rests on a horizontal floor with which it has a coefficient of static friction μ. It is desired to make the body move by applying the minimum possible force F. Find the magnitude of F and the direction in which it has to be applied.
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ANSWER
Normal force,
N=mg−Fsinθ
If F is minimum to move the block, then;
f= frictional force (static)
f=μN=μ(mg−Fsinθ)
For the block to just move,
Fcosθ=f=μ(mg−Fsinθ)
F(cosθ+μsinθ)=μmg
F=
(cosθ+μsinθ)
μmg
If F is minimum, then
let y=cosθ+μsinθ ...........(1) should be maximum
dθ
dy
=−sinθ+μcosθ=0
sinθ=μcosθ
θ=tan
−1
μ
For the value of θ=tan
−1
μ, the force F will be minimum,
and
y=cosθ+μsinθ=cosθ+μ
2
cosθ=cosθ(1+μ
2
)=
(1+μ
2
)
hence, minimum force,
F=
y
μmg
=
(1+μ
2
)
μmg