Question

Two spheres are rolling without slipping on a horizontal floor. They are made of different materials, but each has mass 5.00 kg and radius 0.120 m. For each the translational speed of the center of mass is 4.00 m/s. Sphere A is a uniform solid sphere and sphere B is a thin-walled, hollow sphere. How much work, in joules, must be done on the solid sphere to bring it to rest?How much work, in joules, must be done on the hollow sphere to bring it to rest?

Answer 1

`W_A =  56 J`

`W_B = 66.67 J`

Step-by-step 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
`I_A = 2/5 mR^2`

moment of inertia for hollow sphere is
`I_B = 2/3 mR^2`

As both sphere are moving , thus they possessed transnational and rotational kinetic energy

Total kinetic energy for A

`K_A = (1)/(2) mv^2 +(1)/(2) I \omega^2`

`K_A = (1)/(2) mv^2 +(1)/(2) (2)/(5) mR^2 (V)/(R)^2`

`K_A = \frac{7}[10} mv^2`

`K_A = \frac{7}[10} * 5 * 4^2 = 56 J`

Total kinetic energy for B

`K_A = (1)/(2) mv^2 +(1)/(2) I \omega^2`

`K_A = (1)/(2) mv^2 +(1)/(2) (2)/(3) mR^2 (V)/(R)^2`

`K_A = \frac{5}[6} mv^2`

`K_A = \frac{5}[6} * 5 * 4^2 = 66.67 J`

As sphere finaly come to rest hence final kinetic energy is zero

`W_A = K.E_(final) - K.E_(initial)`

`W_A = 0 - 56 = -56 J`

`W_B = K.E_(final) - K.E_(initial)`

`W_B = 0 - 66.67 = - 66.67 J`