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

Question

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.

Explanation / Answer

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)

adding the three equations:

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

a=2.69 m/s^2

T1=33.77 N

T2=27.47 N

answers:

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 increase.

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