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Three blocks are connected on the table as shown below. The

coefficient of kinetic friction between the block of mass m2 and

the table is 0.310. The objects have masses of m1 = 4.75 kg, m2 =

1.10 kg, and m3 = 2.20 kg, and the pulleys are frictionless.

(a) Draw free-body diagrams for each of the objects.

(b) Determine the acceleration of each object, including its

direction.

m1: ___ m/s2 Direction?

m2: ___ m/s2 Direction?

m3: ___ m/s2 Direction?

(c) Determine the tensions in the two cords.

left cord ____ N

right cord ____ N

(d) If the tabletop were smooth, would the tensions increase,

decrease, or remain the same? Explain.  Edit Comment  Solutions
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let tension in left string is T1.

tension in right string is T2.

let acceleration of whole system is a m/s^2,towards left.

then for m1:

m1*g-T1=m1*a..(1)

for m2:

T1-T2-0.31*m2*g=m2*a..(2)

for m3:

T2-m3*g=m3*a..(3)

g*(m1-0.31*m2-m3)=a*(m1 m2 m3)

a=2.69 m/s^2

T1=33.77 N

T2=27.47 N

b)

m1: 2.69 m/s^2,downwards

m2: 2.69 m/s^2,leftward

m3: 2.69 m/s^2,,upwards

c) left cord=T1=33.77 N

right cord:T2=27.47 N

d)if table were smooth,the friction part will vanish.

then a=g*(m1-m2)/(m1 m2 m3)

=3.1 m/s^2

T2=m3*(g a)=28.38 N

T1=m1*(g-a)=31.8 N

so left cord tension will decrease while right cord tension will

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