Grade 12th passMechanics

Please help me in doing this problem. In the arrangement shown the mass of bar A is m and that of wedge B is M. The masses of the pulley and thread is negligible. Friction is absent. Find the acceleration of the wedge.

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Ankush

9 Years agoGrade 12th pass

3 Answers

Umrao Krishna Singh

9 Years ago

Acceleration of A and B is going to be the same perpendicular to the incline.

Using that I get acceleration of wedge B =

$\frac{mgcos\Theta }{M+m}$

Ankush

9 Years ago

The answer is (mg sin(alpha))/(M+2m(1-cos(alpha))). But I don`t know how to solve . I had not got any solution of this problem.

Umrao Krishna Singh

9 Years ago

Hi, sorry I gave the wrong answer last time. That being said I still don’t get the right one (sorry again!). But anyways method remains same whatever the answer may be. It would have been a lot more helpful if you told us where you are having trouble in finding the answer. Since I don’t have that info, I am going to give you a general direction.

Draw the free body diagram of block A and B. Here you will need to draw 2 FBD for both the blocks, one where forces are resolved along horizontal and vertical, other where forces are resolved along the incline and perpendicular to it.
Form the relevant equations using the horizontal and vertical FBD for block B.
From FBD along and perp. to incline, you have to find the acceleration of blocks A and B perpendicular to incline and make these accelerations equal. This I told you last time too.
By now you should have 3 equations and 3 variables. Just solve them to find the answer.

Using these I get

$a = \frac{mgcos\alpha sin\alpha }{msin^2\alpha +M}$

Try out on your own maybe you’ll get the correct answer. If this still doesn’t help, I’ll post my answer, but it’ll be better if you come upon it on your own, that’s why I didn’t write it this time.