 # Third Law of Motion

• For every action there is an equal and opposite reaction.
• Action and reaction never act on same body.
• Velocity of rocket at any time \tt V = v_o + u \log_{e}\left(\frac{m_{0}}{m}\right)
• When initial velocity is zero. \tt V = u \log \left(\frac{m_{0}}{m}\right)
• Thrust acting on rocket \tt F = - u \left(\frac{dm}{dt}\right)
• For variable velocity \tt \int_{vo}^{v} dv = \int_{mo}^{m} - u \frac{dm}{m}
• Constraint equation
x1 + x2 = R
v1 + v2 = 0
a1 + a2 = 0 •  x1 + x3 = l1
(x1 – x3) + (x4 – x3) = l2
(x1 – x4) + (x2 – x4) = l3
a1 + a3 = 0
a1 + a4 – 2a3 = 0
a1 + a2 – 2a4 = 0 •  In spring Restoring force is directly proportional to elongation.
F ∝ x  ⇒  K = f/x. (K = spring constant)
• Springs connected in series  Keq = K1 + K2
• Springs connected in parallel \tt K_{eq} = \frac{K_{1}K_{2}}{K_{1} + K_{2}}
• K1 x1 = K2 x2

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For every action there is an equal and opposite reaction and both acts on two different bodies. Mathematically F12 = −F21