Two blocks are connected by a massless string over a massless and frictionless p

Question

Two blocks are connected by a massless string over a massless and frictionless pulley. Mass 1 (4 kg) is on a plane inclined at 32 degrees. Mass 2 (10 kg) is hanging from the pulley. The coefficient of static friction is 0.26 and the coefficient of kinetic friction is 0.16 on the surface.

a)The system is released from rest. Do the masses start to slide? Prove your answer.
b)Use Newton's 2nd Law to obtain the equations you will need to solve for acceleration and tension (3 equations)
c)What is the acceleration of the blocks?
d)What is the tension in the string?

Explanation / Answer

The mass of the block m1 = 4kg

the mass of the block m2 = 10kg

the coefficient of static firction s = 0.26

from Newtons' law

m2a = m2g - T = 0

T = m2g = (10)(9.8) = 98 N

and

m1a = T - m1gsin - sm1gcos = 0

        T = (4)(9.8) sin32 + (0.26)(4)(9.8)cos = 0

then T = 8.64 + 20.77

So yes the masses starts slides

(b) From newton's laws

   m2a = m2g - T

then T = m2g - m2a

and

m1a = T - m1gsin - kmgcos

m1a = m2g - m2a - m1gsin32 - (0.16)m1gcos32

(m1 + m2) a = [m2g - m1gsin32 - (0.16)m1gcos32]/(m1 + m2)

a = [(10)(9.8) - (4)(9.8)sin32 - (0.16)(4)(9.8)cos32]/ 14

    =   98 - 20.77- 5.32 = 5.13m/s^2

(b) The tension in the string

      T = (10)(9.8 -5.13) = 46.7 N

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