derive the expressions for acceleration and tension in connected bodies ( m1
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11th
Physics
Laws of Motion
Solving Problems In Mechanics
For mass m, the forces are given as
T−mg=ma ...... (1)
Similarly, for mass M, the forces are given as
Mg−T=Ma ...... (2)
From equation (1), we have
T=mg+ma ...... (3)
Substituting equation (3) in (2) we get
Mg−mg−ma=Ma
g(M−m)=a(M+m)
a=(
M+m
M−m
)g
T=m×(
M+m
M−m
)g+mg
T=
M+m
Mm−m
2
g+mg
T=g(
M+m
Mm−m
2
+m)
T=g(
M+m
Mm−m
2
+m
2
+Mm
)=g(
M+m
2Mm
)
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