A 14kg Box rests on a frictionless surface. It is attached to a 8kg weight by a thin wire that passes over a frictionless pulley. The pulley is a uniform solid disk of mass 3kg and diameter 1m. After the box is released find (a) the tension in the wire on both sides of the pulley, (b) the acceleration of the box, and (c) the horizontal and vertical components of the force on the pulley

(a) Tension on both side of wire

(b) acceleration of the Box

(c) The horizontal and vertical components

Horizontal component

Vertical Component  =130.19 N

Explanation:

Refer attached figure for details.

Applying Newton's 2 law of motion for 14 kg block in horizontal direction

-----------(i)

Similarly, applying Newton's 2 law of motion for 8 kg block in vertical direction

-----(ii)

Consider the case of pulley,

where,

(since mass of the pulley = 3 kg & Radius = 0.5 m)

&

Hence

--------(iv)

Relation between linear acceleration (a) and angular acceleration (α) is as follows,

--------------------(v)

Putting the value of (v) in to (iv)

---------(vi)

adding equation (i),(ii) & (vi) gives

8g =22 a + 1.5 a

now putting the value of a in equation (i) & (ii) we get

= 51.710 N

(a) Hence Tension on both side of wire

(b) acceleration of the Box

(c) The horizontal and vertical components

Horizontal component

Vertical Component = =51.710 + 8 x 9.81 =130.19 N

the area between the graph and the t axis