T=(2m1m2 G)/(m1+m2)?

Aaryanarora246 Aaryanarora246

• 12.04.2018
• Physics
• Secondary School

answered • expert verified How to derive the formula for tension of string in Atwoods Machine: T=(2m1m2 g)/(m1+m2)? See answers RAKSH290 RAKSH290 Let m1>m2 and T be the tension in string so there will acceleration at m1 in downwards and m2 moves upwards ( in Atwood's machine ) then draw fbd ( free body diagrams) for m1 and m2then forces acting on m1 is m1g-T=m1a .............equation 1and forces acting on m2 is T- m2g= m2a...........equation 2now find acceleration ( a ) from eq 1 and 2 from 1, T = m1 (g-a) substitute in 2 I.e.,m1(g-a)-m2g=m2a (m1-m2)g=(m2+m1)a then a = (m1-m2)g/(m2+m1)now substitute acceleration in equation 1 or 2 to get T m1g-T=m1a T =m1(g-a) = m1g- m1(m1-m2)g/(m2+m1) =(m1²g+m1m2g-m1²g+m1m2g )/(m1+m2). T =( 2m1m2g)/(m1+m2) is the required solution MysticalStar07 MysticalStar07

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