Block slipping against two blocks

1. Nov 9, 2016

Vibhor

1. The problem statement, all variables and given/known data

In the setup , block C remains at rest and block A move towards left when system is released . If velocity of A is 'u' towards left at an instant , what is the vertical component of velocity with which B descends .What is the horizontal component of velocity of B at this instant ?

Ans : Vertical component of velocity = (u/2)tanθ1

Horizontal component of velocity = (u/2)

2. Relevant equations

3. The attempt at a solution

Block B is constrained to move along the contact surface with C . From the geometry it can be seen that when B moves vertically down by distance 'x' ,it is constrained to move by a distance xcotθ1 towards left .

By similar argument , suppose C is not present ,and B is somehow constrained to move exclusively in only vertical direction .If B moves down by a distance 'x' , A moves towards left by a distance xcotθ2 .

Combining the two effects we can say if B moves down by a distance 'x' , A moves towards left by a distance xcotθ1 +xcotθ2 .

Similarly If vertical speed of B is 'v' then speed of A is u = vcotθ1 +vcotθ2 .

Now in the question we are given 'u' and asked to find 'v' and 'vcotθ1' .

I am not sure how do I get 'v' and 'vcotθ1' in terms of u .

Is the book answer correct ?

Any help is appreciated .

Thanks .

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Last edited: Nov 9, 2016
2. Nov 9, 2016

haruspex

I agree with your answer. It clearly has to involve θ2. It looks like the problem was originally for two equal angles and the answer was not updated correctly when they were made different angles.