Question

4. [14pts total] In class we solved a variation on the Atwood machine to find the mag- nitude of the acceleration of the masses, a, and the tension in the string connecting them, T. Now consider this arrangement: e me 02 / Figure 1 If we had solved the case shown in Figure 1, where the surfaces are frictionless and the pulley is massless and frictionless, we would have found: (_ (m2 sin 02 – mj sin 01)g (mi + m2) = and T - mim2 (sin 01 + sin (2) (mi + m2) assuming m2 sin 02 > mi sin 01. Now you need to solve the scenario presented in Figure 2, where again the surfaces are frictionless and the pulley is massless and frictionless.

Answer 1

given In scenario infigure t we have a = M2 sin Oz - m, sino) g (m,+ m2) and T- Mima (sind,+ sin 02 g a . (mi +M2) al We can use these equation to obtain expressions for magnitude of acceleration and the tension in the string in fig. 2. We can compare variables from fig s. to fig. 2. in fig 2 in fis 2 lin tig 2 and o m, is equivalent to me in fig 1. mam M2 is equivalent to Ma in fig & m2 =12 o is equivalent to Oz in his f* O₂=0 from g. 't Is zero in figure a ..0,50 putting these values of me, me, o, fO2 in equation 1 we can find magnitude of acceleration - a= (M2 Sino -m, sin(o)g 3 a mi + m₂ but sin(o)=0

faz magasin enda a m(sin o) 9 m, tm @ f putting values of m, ma, 0, fl2 in egr @ we get Ism, Mz Sino) + sino) g met me 'T= m, M2 + (Sinox g mitme 6 for eq2 ③ I unit of a is m/s² Now we will check unit of RHS of eq 2 ③ Unit of Me is kg sind is unitless unit of g is m/s² & unit of my is kg i unit of RHS = kg nmish . By m/s2 (kg+kg) kg . unit of LHS = unit of RHS, for ean 6 Unit of LHS = Unit of T = N = kg m/s² Unit of RHS = kg x kg x m/s² (kg + kg)

- Unit of RHS = kg m 1st - kg m/s2 an *Я. . Unit of LH3 = Onit of RHS. M2 = 2 kg 40=30.04 given m, =3 kg &g=9.8 m/s2 az M₂ g sino mitme - - a= 2x9. 8x Sin3o a= 2x9. 8x Sin 30 372 mis 5 as 19:6* 0.5 m/s2 a) a= 9.8 mes? > ) a= 1.96 m/s2 & T = me Mz g sino mitmz - ! 34 2x 9.8 x Sin 30° 3+2 58.8 * Ons beretz 29.4 kamle TC T55.88 N