First slide

Application of Newtons laws

Question

If the blocks A and B are moving towards each other with accelerations a and b as shown in the figure, find the net acceleration of block C.

Moderate

A

$a \hat{i} - 2 (a + b) \hat{j}$
B

$- (a + b) \hat{j}$
C

$a \hat{i} - (a + b) \hat{j}$
D

None of these

Solution

$From length constraint l_{1} + l_{2} + l_{3} + l_{4} = C$
$\begin{array}{l} l_{1}^{''} + l_{2}^{''} + l_{3}^{l^{'}} + l_{4}^{''} = 0 \\ (- a - b) + 0 + (- a - b) + c = 0 \\ c = 2 a + 2 b \end{array}$
From wedge constraints, acceleration of C is right side is a.
acceleration of C w.r.t. ground $= a \hat{i} - 2 (a + b) \hat{j}$

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