Two blocks of mass m1 and m2 are connected by a cord of negligible mass. Mass m2

Question

Two blocks of mass m1 and m2 are connected by a cord of negligible mass. Mass m2 moves along a slope of inclination of 30degrees while m1 is hanging free. (a) develops expressions for the acceleration, a of the masses and tension, T in the cord. (b) if the masses are equal at 2.0kg each what should be the inclination of the slope for the system to have zero acceleration? (c) if m1 = 2.0kg and m2 = 4.0kg what are the corresponding acceleration and tension in the system? Please clearly show all the work

Explanation / Answer

let T Be the tension acting in the cord

and consider that the block m1 is going downward with acceleration a

m1g-T=m1a.............................(1)

T-m2gsin 30=m2a.........................(2)

adding both equation we get

a=(m1+m2/2)*g/(m1+m2)

T=m1g-m1a

T=m1g(1+(2m1+m2)/(m1+m2))

B)FOR THE SYSTEM TO BE IN EQUILIBRIUM

T=m1g=m2gsin a

sin a=1

a=90 degree

the angle of inclination has to be 90 degree

C)2g-T=2a .................(3)

T-4gsin 30 =4a ...........(4)

adding (3)and (4) we get

4g=6a

a=2/3g=6.533m/s2

T=2g-2a=2g-4/3g=2/3g=6.533m/s2

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