In Figure (a), a constant horizontal force Upper F Over script right-arrow End S

Question

In Figure (a), a constant horizontal force Upper F Over script right-arrow End Scripts Subscript a is applied to block A, which pushes against block B with a 22.0 N force directed horizontally to the right. In Figure (b), the same force is applied to block B; now block A pushes on block B with a 11.0 N force directed horizontally to the left. The blocks have a combined mass of 11.0 kg. What are the magnitudes of (a) their acceleration in Figure (a) and (b) force Upper F Over script right-arrow End Scripts Subscript a ?

Explanation / Answer

in fig (a)

for block B

f = mB*a

f = 22 N

a = 22/mB

on block A

F - f = mA*a

F - 22 = mA*a

F = (mA+mB)*a

F = 11*22/mB..........(1)

in fig (b)

for A

f' = mA*a'

11 = mA*a'

a' = 11/mA

for B

F - f' = mB*a'

F = (mA+mB)*a'

F = 11*11/mA ............(2)

from 1 & 2

mB = 2*mA

mA + mB = 11

mA + 2mA = 11

mA = 11/3 kg

mB = 22/3 kg

part (a)

acceleration a = 22/mB = 3 m/s^2

acceleration a' = 11/mA = 3 m/s^2

part(b)

F = 11*3 = 33 N

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