Respuesta :
Answer:
[tex]W_A = 56 J[/tex]
[tex]W_B = 66.67 J[/tex]
Explanation:
given data:
mass of sphere is 5 kg
sphere A is solid sphere
sphere B is hollow
we know that
moment of inertia for solid sphere is[tex] I_A = 2/5 mR^2[/tex]
moment of inertia for hollow sphere is [tex]I_B = 2/3 mR^2[/tex]
As both sphere are moving , thus they possessed transnational and rotational kinetic energy
Total kinetic energy for A
[tex]K_A = \frac{1}{2} mv^2 +\frac{1}{2} I \omega^2[/tex]
[tex]K_A = \frac{1}{2} mv^2 +\frac{1}{2} \frac{2}{5} mR^2 \frac{V}{R}^2[/tex]
[tex]K_A = \frac{7}[10} mv^2[/tex]
[tex]K_A = \frac{7}[10} \times 5 \times 4^2 = 56 J[/tex]
Total kinetic energy for B
[tex]K_A = \frac{1}{2} mv^2 +\frac{1}{2} I \omega^2[/tex]
[tex]K_A = \frac{1}{2} mv^2 +\frac{1}{2} \frac{2}{3} mR^2 \frac{V}{R}^2[/tex]
[tex]K_A = \frac{5}[6} mv^2[/tex]
[tex]K_A = \frac{5}[6} \times 5 \times 4^2 = 66.67 J[/tex]
As sphere finaly come to rest hence final kinetic energy is zero
[tex]W_A = K.E_{final} - K.E_{initial}[/tex]
[tex]W_A = 0 - 56 = -56 J[/tex]
[tex]W_B = K.E_{final} - K.E_{initial}[/tex]
[tex]W_B = 0 - 66.67 = - 66.67 J[/tex]
