Objects with masses m1 = 8.0 kg and m2 = 4.00 kg are connected by a light string that passes over a frictionle

Question

Objects with masses m1 = 8.0 kg and m2 = 4.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.30. If, when the system starts from rest, m2 falls 1.00 m in 1.50 s, determine the coefficient of kinetic friction between m1 and the table.

http://i141.photobucket.com/albums/r75/Roach131313/p4-30.gif

Answer 1

Look at a FBD of each mass

m1:
m1*a=T-f
where T is the tension in the string and f is friction

m2:
m2*a=m2*g-T

using the displacement info
V(t)=m2*a*t

y(t)=.5*m2*a*t^2

assuming down as positive

y(1.5)=1
1=.5*4*a*1.5^2
a=2/(4*1.5^2)
a=2/9

now that you know a, solve for f
m2*a=m2*g-T
T=m2*(g-a)

m1*a=T-f
T=m1*a+f

m2*(g-a)=m1*a+f
f=m2*(g-a)-m1*a

f=4*(9.81-2/9)-8*2/9
f=36.57

f=N*u
where N is the Normal force m1*g
and u is the coefficient of kinetic friction
u=36.57/(8*9.81)
=.466

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