Question

three identical blocks each of mass 10kg are pulled as shown on the horizontal frictionless surface. if the tension in the rope 30n. what is the acceleration of each block? and what are the tensions in the other ropes? (neglect the masses of the ropes)

Answer 1

Given:
Masses = m1=m2=m3 = 10kg
Force =30N
Acceleration of system of three blocks A,B,C = Force/TOTAL mass
a=F/m1+m2+m3
=F/10+10+10
=F/3m
=30/30
=1 m/s2
Tension in rope A:
T= ma
=10x1=10N

Tension in rope B:
T=( m1+m2)a
=(10+10)x1
=20N

Tension in Rope C:
T= (m1+m2+m3)×a
=(10+10+10)x1
=30N

Answer 2

Given:

Force (F)=30N
Masses (m1) =10 kg , (m2)=10 kg ,  (m3)=10 kg

Total mass = m1+m2+m3 = 10+10+10=30kg

Acceleration (a) of 3 blocks= force(F) / Total mass

Acceleration (a) of 3 blocks= 30 / 30 = 1 m /s^2

Tension in 1st rope = (m1)(a)
  T1   =10*1= 10N

Tension in 2nd rope= (m1+m2)*a
 T2   =(10+10) *1= 20*1= 20 N

Tension in 3rd rope=(m1+m2+m3)*a
 T3  =(10+10+10)*1= 30*1= 30N

----------------------------------------------------------------------------------------------------

Acceleration of 3 blocks = 1 m/s^2
T1 = 10N
T2= 20N
T3= 30N
------------------------------------------------------------------------------------------------------