Question

In figure (a) a constant horizontal forceF_a is applied to block A,which pushes against block B with a 26.0 Nforce directed horizontally to the right.In figure (b), the same forceF_a is applied to block B; nowblock Apushes on block B with a 13.0 N force directed horizontally to the left.The blocks have a combined mass of 21.0 kg.(a) What is the magnitude of the accelerationof the blocks in figure (a)?
m/s²

(b) What is the magnitude of the forceF_a?
N

Answer 1

a) pretty simple just use Newton's second law.F=maa=F/m=1.23 m/s²b) The Force of F_a is still the same (26N) if youneed to know the net force on block B just add the vectors.F_n=F_a+F_b=13N

Answer 2

in figure (a),
use F = ma for A + B, F_a =(21.0kg)*a(1)
use F = ma for B, 26.0 = m_B* a(2)
in figure (b)
use F = ma for A + B, F_a = (21.0kg)*a'(3)
use F = ma for A, 13.0 =m_A*a'(4)
compare (1) and (3), a = a'
(2)'(4): 2 = m_B/m_A, m_B =2m_A, so m_A = 7.0 kg, m_B = 14.0kg,
from (2) a = 26.0/14.0 = 1.86 m/s²
from (1) F_a = 39 N