The following system accelerate to the right when released from rest. Consider t

Question

The following system accelerate to the right when released from rest. Consider the pulley to be massless and frictionless and the cold is massless. The coefficient of kinetic friction between Mock A and the surface mu = 0.26. The interface between block Band the surface is frictionless. The mass of block A is 1.0 kg. the mass of block B is 4.0 kg and the angles of the inclines arc both 12 from the horizontal. Find the magnitude of the acceleration of the system. Find the magnitude of the tension in the cord. How much would the acceleration of the system change by if the surface under block A was lubricated to that the interface between Mock A and the surface was frictionless?

Explanation / Answer

Let acceleration of system is a.

force on B:

4*a=4*9.8*sin-T--------------(1)

Force on A:

Friction force acting = 0.26*1*9.8*cos

Force balancing:

T-0.26*1*9.8*cos-1*9.8*sin=1*a----------(2)

using T from (1) in (2):

4*9.8*sin-4*a-0.26*1*9.8*cos-1*9.8*sin=1*a

4*9.8*sin12-4*a-0.26*1*9.8*cos12-1*9.8*sin12=1*a

4*9.8*sin12-0.26*1*9.8*cos12-1*9.8*sin12=5*a

3.6203=5*a

a= 0.7241 m/s^2

(A)

Acceleration of system =  0.7241 m/s^2

(B)

T=4*9.8*sin-4*a

=4*9.8*sin12-4*0.7241

= 5.25374 N

(C)

When there is no friction then;

4*a=4*9.8*sin-T--------------(3)

T-1*9.8*sin=1*a----------(4)

using T from (3) into (4)

4*9.8*sin-4*a-1*9.8*sin=1*a

4*9.8*sin12-1*9.8*sin12=5*a

6.1126=5*a

a= 1.2225 m/s^2

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