Question

The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is $16.0N$ when the system is set into 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

Answer 1

The correct option is A 19.6 J

Given that,

Tension T = 16.0 N

Now,

$T-2mg+2ma=\mathrm{0....}\left(I\right)$

$T-mg-ma=\mathrm{0....}\left(II\right)$

From equation (I) and (II)

$3ma-mg=0$

$g=3a$

$a=\frac{g}{3}$

Now, put the value of g in equation (II)

$T-3ma-ma=0$

$T=4ma$

$a=\frac{T}{4m}$

Now, from equation of motion

At $t=1$

$s=ut+\frac{1}{2}a{t}^2$

$s=0+\frac{1}{2}\times \frac{T}{4m}\times {\left(1\right)}^2$

$s=\frac{16}{8m}$

$s=\frac{2}{m}$

Thus, change in the height of the block will be;

$\Delta h=s$

Net mass

$2m-m=m$

Now, decrease potential energy

$P.E=mg\Delta h$

$P.E=m\times 9.8\times \frac{2}{m}$

$P.E=19.6J$

Hence, the decrease potential energy is $19.6J$