Answer to Question #105197 in Classical Mechanics for Arjo Joseph

Question

7. A mass (M1 = 5 kg) is connected by a light cord to a mass (M2 = 4 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius=0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley?

8. A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 200 Kg and a radius of 2 m. A 40-Kg child rides at the center of the merry-go-round while a playmate sets it turning at 0.35 rev/sec. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning? (HINT: Treat the child as a particle)

Answer 1

As per the given question,

mass of the object $(M_1)=5 kg$

mass of the second object $(M_2)=4kg$

Radius of the pulley (R)=0.2m

Acceleration of the object $(a)=3.5 m/sec^2$

Now,

Let the tension in the string between the pulley and block $M_1$ is $T_1$ and tension in the string between the pulley and block $M_2$ is $T_2$

So, $M_1g-T_1=M_1a------(i)$

$T_2= M_2a--------(ii)$

Now from the torque equation on the pulley

$(T_1-T_2)R=I\alpha-----(iii)$

Now, substituting the given value in the equation (ii)

$T_2=4\times 3.5= 14.0N$

Now, substituting the given values in the equation (i)

$5\times 9.8-T_2=5\times 3.5$

$\Rightarrow T_1=31.5N$

Now, substituting the values in the equation (iii)

$\Rightarrow (31.5-14)\times 0.2=I\dfrac{a}{R}$

$\Rightarrow I =\dfrac{17.5\times 0.2\times0.2}{3.5}=0.2 kg-m^2$