A) Two blocks are being pushed across a horizontal floor with a coefficient of k

Question

A) Two blocks are being pushed across a horizontal floor with a coefficient of kinetic friction m=.3 . The mass of block A is 3kg, and the mass of block B is 2 kg. If the force applied by the finger is F=20N, what is the acceleration of the blocks?

B) A block of mass 3.3 kg is suspended by two ropes as shown in the picture below. The angle that the left rope makes with the horizontal is q= 40 degrees. The angle that the right rope makes with the horizontal is q= 30 degrees. If the maximum tension EITHER rope can withstand is 50 N, what is the maximum mass that can be supported in this situation?

C) A block with mass M = 4 kg is held against a vertical wall by a horizontal force F = 75 N. The wall has coefficient of static friction m = .6. The force F is reduced to only 60 N and it is seen that the block accelerates down with a = 2 m/s2. What is the coefficient of kinetic friction between the block and the wall?

Explanation / Answer

NOrmal reaction on block A = 3*9.8 = 29.4 N
Friction = Na * mu = 8.82 N
Normal reaction on B = 2*9.8 = 19.6 N
Friction = .3 * Nb = 5.88 N

a) From newtons second law
F = 20 - mu(Na + Nb) = (Ma + Mb)*a
a = 1.06 m/s/s

b) :et the mass be M
From newton's second law
T*sin(30) + T'*sin(40) = m*g
where T' is tension in the rope making 40 deg with the horizontal
and T is the tension in the rope making 30 deg with the horizontal
Now, T'cos(40) = Tcos(30)
so, T*sin(30) + Tcos(30)*sin(40)/cos(40) = m*g
now, T' = 50 N
T = 44.22 N
m = 5.536 kg

c) Normal = F = 60 N
Friction, f = F*mu = 60*mu
now from newton's second law, mg - 60*mu = ma
mu = 0.52

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