A marble block of mass m1 = 559.1 kg and a granite block of mass m2 = 128.4 kg are connect...

Research:

The gravitational force of the two blocks will be resolved into horizontal and vertical components. There exists a tension force in the rope and the frictional force is directed in a direction opposite to the motion of the blocks. Using Newton’s second law, we calculate the acceleration of the marble block.

Sketch:

The following free body diagrams shows the forces acting on the two blocks,

Simplify:

Given data

Mass of the marble block is,

Mass of the granite block is,

Angles of inclination are, and

Coefficient of friction between the plane and is,

Coefficient of friction between the plane and is,

Let the acceleration of the blocks be ‘a’

Using Newton’s second law we calculate the net force acting on the two blocks.

Net force acting on along x axis is,

…… (1)

Net force acting on along y axis is,

Substitute the value of normal force in equation (1), we get

…… (2)

Net force acting on along x axis is,

…… (3)

Net force acting on along y axis is,

Substitute the value of normal force in equation (3), we get

…… (4)

Calculate:

We get the expression for the acceleration by equating equations (2) and (4), and substituting the values in that expression evaluates the acceleration of the marble block,