An atwood machine consists of two masses hanging from the...

An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The masses have the values M₁ = 27.0 kg and m₂ = 11.0 kg. Assume that the rope and pulley are massless and that there is no friction in the pulley. What is the magnitude of the masses' acceleration a? What is the magnitude of the tension T in the rope?

Transcript

00:01 Hey everyone, welcome back.

00:01 In this question we are given with the edwood machine, as you can see in this particular diagram.

00:07 And we have to find out the acceleration and tension in the ropes.

00:11 So we have considered that mass 1 is greater than mass 2 and tension in the string is t, both the sides.

00:19 And this will be pulled towards center of earth with the force m2g and this one with the force m1g.

00:26 Okay, so since m1 is greater, so this system will accelerate, in this direction and this block will move in the upward direction with same acceleration a since these two are connected with same string so if i try to write the equation of net force then for m1 this will be m1g minus t is equal to m1a and for m2 this can be written as t minus m2g is equals to m2a so i have considered this as equation number one and this one as equation number two if i add these two then i will be having m1 minus m2 into g is equals to m1 plus m2 into a so from here the acceleration of system is coming out as m1 minus m2 into g divided by m1 plus m2 now if i put this value of acceleration here then i can find out the value of tension as g into m1 minus m1 minus m2 divided by m1 plus m2 so this is the acceleration this is the tension so if i simplify this then this is coming out as this will come out as g into this will become so basically i forgot one m1 so here if this is m1 a then i have to multiply this with m1 so i can take out m1 also common so here we will have one and here i will have m1 g so again this is m1 g and this will become m1 plus m2 minus m1 plus m2 divided by m1 plus m2 so here this positive not positive m2 but instead there's positive m1 and negative m1 will cancel out so we will have the value of tension as 2 m1 m2 divided by m1 plus am 2 so this is the value of tension and that must be multiplied with g 2 m1m2 g over m1 plus m2 this is the value of tension and this one is the value of acceleration now in this question we are given with the value, so here the value of m1 is 27 kg and that of m2 is 16 kg...

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