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arindameducationusc
 one year ago
Lets Discuss about Tension...
(Tutorial)
arindameducationusc
 one year ago
Lets Discuss about Tension... (Tutorial)

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arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\(\Huge\color{red}{Tension} \) When a string, thread or a rod is stretched, a force comes into play known as tension. It is \(\Large\color{blue}{pulling} \) in nature.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9Consider a block connected with a string such that other end of string is connected with a fixed platform. dw:1440745098195:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9Example=>dw:1440745678272:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9now, for m1dw:1440745834828:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9now for m2, dw:1440745871420:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9now for pulley, dw:1440745915192:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9now for fixed pulley, dw:1440745990880:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\(\Large\color{blue}{At~wood~machine} \) dw:1440755955813:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9In the figure shown a mass less and an inextensible chord passes over a mass less and smooth pulley suspended from a fixed platform. The two ends of chord carries two blocks m1 and m2. If we assume m1>m2, then block m1 moves downward and m2 upward with same acceleration a. Consider a portion PQ on the right side of pulley. Let Tp and Tq be the tension ends of portion PQ dw:1440757592023:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9The portion PQ has same acceleration in downward direction. Therefore TqTp=(mass of PQ)*a TqTp=0*a Tp=Tq The tension at every point of chord on the right side of pulley is samee.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9now for acceleration, For that let T be the commonn tension at every point of string.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9FBD( free body diagram) of m1 dw:1440758339625:dw

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9Equation of motion of m1=> m1gT=m1a (Eqn1)

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9FBDof m2dw:1440758643802:dw Tm2g=m2a (eqn 2)

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9Adding equation 1 and 2 (Use mathematics :D) we get a=(m1m2)g/m1+m2 here m1>m2 //if you are not able to solve let me know, I will solve it.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\[a =\frac{ (m _{1}m_{2} )g}{ m _{1}+m _{2} }\] here m1>m2 Putting the value of a in equation 1 \[m _{1}gT=m _{1}\frac{ (m _{1} m _{2})g}{ m _{1}+m _{2} }\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9we get \[T=\frac{ 2m _{1} m _{2}}{ m _{1} +m _{2}} g\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\(\Large\color{red}{Some~formula~for~certain~cases} \) Well please \(\Large\color{blue}{try~deriving} \) I will just be giving you direct formulas. If you have any problem please contact me, I will definitely help!

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9Case1) is simple (which I did above) dw:1440764462862:dw \[a=\frac{ m _{1} gm _{2}g}{ m _{1}+m _{2}}\] Always remember \[a=\frac{ Net~pulling~force }{ Total~mass~of~system}\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\(\Large\color{blue}{Case ~2} \) dw:1440764771203:dw \[a=\frac{ m _{1}gm _{2} g}{ m _{2} }\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.9\(\Large\color{blue}{Case~3} \) dw:1440764887925:dw \[a=\frac{ m _{2} gm _{1}g}{ m _{1} +m _{2}}\]