Answer:
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