The 12-lb block B starts from rest and slides on the 30-lb wedge A, which is supported by a horizontal surface. Neglecting friction, determine (a) the acceleration of the wedge, and (b) the acceleration of the block relative to the wedge.

the acceleration of the wedge

the acceleration of the block relative to the wedge is

Explanation:

Let assume that the angle at which the block starts to slide is 30°

Given that ;

the weight of block B = =  12-lb

the weight of wedge A = = 30-lb

The 12-lb block B starts from rest and slides on the 30-lb wedge A, which is supported by a horizontal surface.

We can resolve the equation of motion  for the wedge and the block into the vertical component and horizontal components as follows:

From equation (1)

From equation (3) ; we have:

replacing    in  above equation (3); we have :

Making the subject of the formula; we have :

where ; g =

the weight of block B = =  12-lb

the weight of wedge A = = 30-lb

Solving for the acceleration of wedge A  ; we have;

Thus; the acceleration of the wedge

To determine  the acceleration of the block relative to the wedge ; Let consider equation 2

From equation 2;

we know that:

g = 32.2 ft/s²

Thus;

Thus; the acceleration of the block relative to the wedge is

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