Question

Find the acceleration of the $500g$ block in the figure.

Answer 1

The acceleration of the block $500g$ will depend upon the forces acting on the mass in the whole system. By considering the force representation on each block using a free body diagram the acceleration of the block can be calculated easily. FBD is a good way to analyze the forces experienced by a material.

Complete answer:
Every object on earth experiences an attractive force which is known as gravitational force. And when an object is attached to a string a tension force along the string.
In the system of masses mentioned the question there are three masses that experience forces. So the free body diagram of the three blokes can be individually studied as,
A. Free body diagram of the $500g$ block is given as,

The equilibrium force equation of the$500g$ block can be written as,
$0.5\times 10-{{T}_{1}}=0.5a\quad ......(1)$

B. Free body diagram of the $100g$ block is given as,

The equilibrium force equation of the $100g$ block can be written as,
$\begin{aligned} & {{T}_{2}}-{{T}_{1}}-0.1g\sin 30{}^\circ =0.1a \\\ & {{T}_{2}}-{{T}_{1}}-\dfrac{1}{2}=0.1a\quad ......(2) \\\ \end{aligned}$

C. Free body diagram of the $50g$ block is given as,

The equilibrium force equation of the$50g$ block can be written as,
$\begin{aligned} & {{T}_{2}}-0.05g=0.05a \\\ & {{T}_{2}}-0.5=0.05a\quad ......(3) \\\ \end{aligned}$
From adding equation (1), (2), and (3) and simplifying the equation we found an equation that,
$\begin{aligned} & 5-\dfrac{1}{2}-0.5=0.65a \\\ & \Rightarrow 0.65a=4 \\\ & \therefore a=6.15m{{s}^{-2}} \\\ \end{aligned}$
Thus the required answer to the question is $6.14m{{s}^{-2}}$.

Note:
Pulley is a ring-like structure that can roll easily. These are used in mechanical assemblies where we have to move a certain object using strings or ropes. Their main function is to reduce friction and increase mobility.