A 2 kg block is placed over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to the upper block. Take g = 10 m/s2.
None of these
Step 1: to check if sliding is happening. Assume sliding is not happening, and they are moving with an acceleration a,
Block A,∑fx=mAa
⇒12−f=mAa......(1)
Block B,∑fx=mAa
⇒f=mAa.....(2)
Adding (1)and (2)
12=(mA+mA)a
⇒12=(2+4)a
12=6a
⇒a=2m/s2
From (a)
f=4× 2 =8N
but fmax=μ×N
∴ For them to move together without slipping, friction force required is 8N but maximum value of friction is 4N. ∴ our assumption, that, they do not slip is wrong, and f=fmass=4N
∴ For block A,
12−f=mAaA
⇒12−4=2aA
⇒8=2aA
⇒aA=4m/s2
Similarly for block,B,
f=mBaB
⇒ 4=4aB ⇒ aB=1m/s2
From (a)
f = 4 × 2 = 8 N
but fmax = μ× N
= 0.2 × 20 = 4 N
∴For them to move together without slipping, friction force
required is 8N but maximum value of friction is 4N. ∴our
assumption, that, they do not slip is wrong,and f = fmax = 4N
∴For block A,
12 - f = mA/aA
⇒ 12 - 4 = 2 aA
⇒ 8 = 2 aA
⇒aA = 4 m/s2
Similarly for block, B,
f = mBaB
⇒ 4 = 4 aB ⇒aB = 1
m/s2