Question

What is the total energy of the segment, given that mass is 3.9 kg, Vx is 1.45 m/s, Vy is 2.78 m/s, moment of inertia is 0.0726 kg-m^2, angular velocity is 9 rad/s and the height of the center of mass is 0.67m?

Answer 1

To solve this problem we will apply the concepts given by linear kinetic energy and rotation, as well as that of Potential Energy.

In turn, to find the net velocity, it will be necessary to use the vector expression that allows us to find the total magnitude from two components, that is,

`v_x = 1.45m/s`

`v_y = 2.78m/s`

`|v| = √(v_x^2+v_y^2)`

`|v| = √(1.45^2+2.78^2)`

`|v| = 3.1354m/s`

The accumulation of total energy on the body, must be the sum of the three energies mentioned above therefore

`\Delta E = PE + KE_(kinetic) + KE_(Rotational)`

`\Delta E = mgh + (1)/(2) mv^2 + (1)/(2) I\omega^2`

Replacing we have,

`\Delta E = (3.9)(9.8)(0.67)+ (1)/(2) (3.9) (3.1354)^2 + (1)/(2) (0.0726)(9)^2`

`\Delta E = 47.717J`

Therefore the total Energy of the segment is 47.7J