A block (M_A = 30 kg) is on a frictionless horizontal surface and is connected t

Question

A block (M_A = 30 kg) is on a frictionless horizontal surface and is connected to a second block (M_B = 85 kg) which is on an incline with an angle of 25 degrees. The coefficient of kinetic friction between M_B and the incline is 0.15. a) Using Newton`s Second Law, write down the equations that will allow the determination of the motion of the blocks. b) Solve the equations in order to determine an expression for the acceleration of the blocks in terms of Ma, Mb, o, qk, and g. c) Determine the acceleration of the blocks and the tension in the string.

Explanation / Answer

a) on block sitting on incline in vertical direction,

N - m_Bgcos25 = 0

N = m_B gcos25

friction f = uk N = u m_B gcos25 = 113.36 N

on block B along the incline,

m_B gsin25 - T - u m_ B gcos25 = m_B a   ...........(i)

on block A,

T = m_A a   ......(ii)

from(i) and (ii) ,

m_Bg sin25 - u m_Bgcos25 = (m_A + m_B)a

a = m_Bg ( sin25 - ucos25) / (mA + mB)

c) a = 85 x9.81 ( sin25 - 0.15cos25) / ( 30 + 85)    =2.08 m/s^2

T = mAa = 30 x 2.08 = 62.36 N

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