Question

A sphere of uniform density with mass 26 kg and radius 0.5 m is spinning, making one complete revolution every 0.4 s. the center of mass of the sphere has a speed of 5 m/s. (a) what is the rotational kinetic energy of the sphere? 801.09 incorrect: your answer is incorrect. j (b) what is the total kinetic energy of the sphere?

Answer 1

(a) Rotational kinetic energy = 1/2Iω^2

Where, I = cmr^2 = 2/5*26*0.5^2 = 2.6  kg/m^2; ω=1 rev/0.4 sec = 2.5 rev/sec = 2.5*2π rad/s = 15.71 rad/s

Therefore, Rotational KE = 1/2*2.6*15.71^2 = 320.76 J

(b) Total kinetic energy = Linear KE+ Rotational KE
Linear KE = 1/2mv^2 = 0.5*26*5^2 = 325 J
Then,
Total KE of sphere = 320.76+325 = 645.76 J

Answer 2

Part A: The rotational kinetic energy of the sphere is 320.437 J.

Part B: The total kinetic energy of the system is 645.437 J.

What is kinetic energy?

The kinetic energy of an object is defined as the energy of the object due to its motion.

Given that the radius r is 0.5 m and the mass m of the sphere is 26 kg. The center of mass of the sphere has a speed v of 5 m/s and it completes one revolution in 0.4 seconds.

The angular velocity $\omega$ of the sphere is given as,

$\omega = \dfrac { 1 \;\rm revolution}{0.4 \;\rm s}$

$\omega = {2.5}\;\rm rev/s$

$\omega = 2.5 \times 2\times 3.14 \;\rm radian/s$

$\omega = 15.7 \;\rm radian/s$

The angular moment of inertia of the sphere is given as below.

$I =\dfrac {1}{2.5 \;\rm revoution} mr^2$

$I = \dfrac {26 \times 0.5^2}{2.5}$

$I = 2.6 \;\rm kg m^2$

Part A: Rotational Kinetic Energy

The rotational kinetic energy of the system is given below.

$KE_r = \dfrac {1}{2}I\omega^2$

$KE_r = \dfrac {1}{2} \times 2.6 \times 15.7^2$

$KE_r = 320.437 \;\rm J$

Hence, the rotational kinetic energy of the sphere is 320.437 J.

Part B: Total Kinetic Energy

The total kinetic energy of the system is given as,

$KE_t = KE_l + KE_r$

Where KE_t is total kinetic energy and KE_l is the linear kinetic energy of the system.

$KE_t = \dfrac {1}{2}mv^2 + 320.437$

$KE_t = \dfrac {1}{2}\times 26\times 5^2 + 320.437$

$KE_t = 325+320.437$

$KE_t = 645.437 \;\rm J$

Hence we can conclude that the total kinetic energy of the system is 645.437 J.

To know more about kinetic energy, follow the link given below.

https://brainly.com/question/999862.