Ablock of mass m1 = 3.7 kg on a frictionless plane inclined at angle =30o is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.3 kg. what are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord?

a) 0.74m/s^2

b) going down

c) 21N

Explanation:

To have a better understanding of this problem is necessary to draw a free body diagram.

Analysing the m1 box:

and for m2:

the acceleration is negative because we assume is going downward

because the tension is the same we can substitude one formula into the other.

because the acceleration is positive the assumption was right.

The m1 block is going up and the m2 block is going down.

if we take a look of the m2 box:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .