Three blocks A,B and C with masses of 4kg,8kg and 12kg, respectively, are connected by a string. A horizontal force F is applied to block C. What value of F is needed (a) to just start the motion of the blocks and (b) to keep the blocks moving at a constant speed once they start moving? For each case, find the tension in the strings connecting the masses. The coefficients of static friction and kinetic friction between the blocks and the floor are 0.5 and 0.3, respectively.
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Answer:
Given : M
A
=4 kg,M
B
=2 kg,M
C
=1 kg
Step 1 : Acceleration of all the blocks
From figure, we see that the blocks A, B and C will move with a common acceleration a.
By Newton's Second Law, Acceleration =
M
total
F
net External
⇒a=
M
A
+M
B
+M
C
F
a=
4+2+1
14
=2m/s
2
Step 2 :Draw free body diagram for block A [Refer figure]
Step 3 : Apply newton’s law on block A :
ΣF=ma
⇒14−N
AB
=4a
A
Substitute the value of a
A
=a=2m/s
2
:
⇒N
AB
=14−8=6N
Explanation:
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