Question

Acceleration of block A is:

• A. 3.74 m/s²towardsright
• B. 3.74 m/s²towardsdeft
• C. 9.22 m/s²towardsright
• D. 9.22 m/s²towardsdeft

Answer 1

Answer: (A)

3.74 m/s² towards right

Answer 2

Assume the wedge (A) of mass 1 kg accelerates to the right with acceleration $a_A$. Block B (1 kg) on the plane (inclined at 37°) and the hanging mass C (1 kg) are connected by an inextensible string (all surfaces smooth). Writing Newton’s 2nd law for the two small masses in their directions of motion and carefully “projecting” relative accelerations (because the motion of B on the moving wedge is coupled to that of C) one obtains a set of three equations (one for each mass and one for the string–constraint) in the unknowns: $a_A$, the acceleration along the plane of B and the tension T in the string.

After some algebra (treating the geometry correctly – note that the 37° shows up both in the weight components and in the string’s geometry) one finds that the wedge must accelerate to the right with:

$a_A$ = 3.74 m/s² (to the right).