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The heavier block is an Atwood machine that has a mass twice that of the lighter one. The tension in the string is 16.0N when the system is set into the motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.
(A) 19.6 J
(B) 29 J
(C) 35 J
(D) 10 J

seo-qna
Last updated date: 16th Jun 2024
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Answer
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Hint We should know that potential energy is defined as the energy that is stored in any system. The potential energy is defined as the measurement of the amount of work done by the system. The potential energy is altered usually on the basis of the equilibrium position and also the virtue of the position of the system.

Complete step by step answer
We should know that,
Tension is denoted by T which is 16.0 N.
Now,
$T - 2mg + 2ma = 0...........(i)$
$T - mg - ma = 0..........(ii)$
From the equations we can say that:
$3ma - mg = 0$
Now we have to evaluate to get:
$g = 3a$
$\Rightarrow a = \dfrac{g}{3}$
Now we have to put the value of g in the equation (ii) to get:
$T - 3ma - ma = 0$
$\Rightarrow T = 4ma$
$\Rightarrow a = \dfrac{T}{{4m}}$
Now, from the equation of motion we get that at t = 1:
$s = ut + \dfrac{1}{2}a{t^2}$
$\Rightarrow s = 0 + \dfrac{1}{2} \times \dfrac{T}{{4m}} \times {(1)^2}$
So, we have to find the value of s as:
$s = \dfrac{{16}}{{8m}}$
$\Rightarrow s = \dfrac{2}{m}$
Thus, we can say that change in the height of the block will be:
$\Delta h = s$
The net mass is given as:
$2m - m = m$
So, the decrease of the potential energy is given as:
$P.E. = mg\Delta h$
$\Rightarrow P.E. = m \times 9.8 \times \dfrac{2}{m}$
$\Rightarrow P.E. = 19.6J$
Hence, the decreased potential energy is 19.6 J. So,

the correct answer is given as option A.

Note It should also be known to us that potential energy is the energy which is held against an object because of the position which is relative to the other objects, and then stress itself, the electric charge and various other factors.