Problem #11 (Due 10/14 Friday by 8:00 a.m.) A 4.0 kg block is at rest on an incl

Question

Problem #11 (Due 10/14 Friday by 8:00 a.m.)
A 4.0 kg block is at rest on an inclined plane that makes an angle fo 30.0o with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is 0.24. The block is attached to a second block of mass 5.0 kg that hangs freely by a string that passes over a frictionless and massless pulley.
a) Draw a free body diagram and sum forces for each mass.
b) Find the acceleration of the masses and the tension in the cord.

*****My specific question is on part b. of finding the acceleration. Any help would be greatly appreciated! Thanks so much!

Explanation / Answer

tension in cord= 5(g -a) where a=accelaration of both blocks

for 4 kg block
N= mgcos30= 4*9.8*cos30= 33.948N
and frictinal force=N= 8.147 N

and force along incline = mgsin30= 19.6

also, for the 4 kg block

T-friction-gravity along incline= mass*acc

T-8.147-19.6=4a

as T=5(9.8-a)

5(9.8-a)- 27.747= 4a

solving for a

a= 2.361 m/s*s

and tension= 5(9.8-a)= 5*(9.8-2.361)= 37.192 N

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