Question

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 x 10^-3 kg∙m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is:
Select one:

a. the heavier block

b. none (all three objects have the same kinetic energy)

c. none (all three objects have the same kinetic energy)

d. either block (the two blocks have the same kinetic energy)

e. the pulley

Answer 1

Answer:

maximum kinetic energy is for Pulley

e) The pulley

Explanation:

Let 4 kg block is moving downwards with speed "v" so we can say that 2 kg block will move upwards with same speed "v"

Now we know that pulling is in pure rotational motion

so we will have

$\omega = \frac{v}{R}$

$\omega = \frac{v}{0.03}$

now kinetic energy of each is given as

For 4 kg block

$K_1 = \frac{1}{2}(4)(v^2) = 2v^2$

for 2 kg block

$K_2 = \frac{1}{2}(2)(v^2) = v^2$

For pulley

$K_3 = \frac{1}{2}I\omega^2$

$K_3 = \frac{1}{2}(4.5\times 10^{-3})\frac{(v^2)}{0.03^2}$

$K_3 = 2.5 v^2$

So maximum kinetic energy is for Pulley