A particle of mass 2kg rests on a rough horizontal surface which has a coeffcient of friction 0.3. Find the least force required to move the particle when it is

a) pulling horizontally

b) pulling upwards at an angle of 30 degree to the horizontal

c) pushing downwards at an angle of 45 degree to the horizontal

Take g=10m/s2

Update:

a) pulling horizontally (6N)

b) pulling upwards at an angle of 30 degree to the horizontal(5.9N)

c) pushing downwards at an angle of 45 degree to the horizontal

Take g=10m/s2

Rating

(a) Maximum friction = μmg where μ = coefficient of friction

So, when pulling horizontally:

Max. friction = 0.3 x 2 x 10 = 6 N

(b) Suppose the pulling force magnitude = F, then:

Normal reaction of the surface on the block = mg - F sin 30 = mg - F/2 (F sin 30 being the vertical upward component of F on the block)

Therefore, the necessary condition for moving the block will be:

0.3 x (mg - F/2) <= F cos 30

6 - 0.15 F <= 0.866 F

6 <= 1.016 F

F >= 5.9 N

(c) Suppose the pushing force magnitude = F, then:

Normal reaction of the surface on the block = mg + F sin 45 (F sin 45 being the vertical downward component of F on the block)

Therefore, the necessary condition for moving the block will be:

0.3 x (mg + F sin 45) <= F cos 45

6 + 0.212 F <= 0.707 F

6 <= 0.495 F

F >= 12.1 N

Source(s): Myself