## Laws of Motion

# 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

x_{1}+ x_{2}= R

v_{1}+ v_{2}= 0

a_{1}+ a_{2}= 0

- x
_{1}+ x_{3}= l_{1}(x_{1}– x_{3}) + (x_{4}– x_{3}) = l_{2}(x_{1}– x_{4}) + (x_{2}– x_{4}) = l_{3}a_{1}+ a_{3}= 0

a_{1}+ a_{4}– 2a_{3}= 0

a_{1}+ a_{2}– 2a_{4}= 0

- In spring Restoring force is directly proportional to elongation.

F ∝ x ⇒ K = f/x. (K = spring constant)

- Springs connected in series K
_{eq}= K_{1}+ K_{2} - Springs connected in parallel \tt K_{eq} = \frac{K_{1}K_{2}}{K_{1} + K_{2}}
- K
_{1}x_{1}= K_{2}x_{2}

### View the Topic in this video From 44:19 To 57:09

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

For every action there is an equal and opposite reaction and both acts on two different bodies. Mathematically **F**_{12} = −**F**_{21}