Question

A 45 wedge is pushed along a table with constant acceleration

a. A block of mass m slides without friction on the wedge. Find its acceleration. Gravity is directed down

Answer 1

Answer:

a = ½ ( A + g )

Explanation:

To understand the question, first see the figure attached to get the scenario.

Now the total force acting on the block which is not only going down at an angle but it is also pushed forward by wedge moving with acceleration A is;

ma = F(total)  x sin Θ

ma = (mAsin Θ + mgcos Θ) sin Θ

a = (Asin Θ + gcos Θ) sin Θ

a = A 〖Sin〗^2 Θ + g cos Θ sin Θ

Here Θ = 45

Putting the value and simplifying ;

a = ½ ( A + g )