Question

A basketball rolls across a floor without slipping, with its centerof mass moving at a certain velocity. A block of ice of the samemass is set sliding across the floor with the same speed along aparallel line.(a) How do their energies compare?(b) How do their momenta compare?(c) The two objects encounter a ramp sloping upward.

Answer 1

Answer:

In order to understand all three questions one must have knowledge of rotational and transitional motion.

Explanation:

a.

Both energies could be compared by means of their motion,as Ball it self rolling and also moving linearly therefore it has combination of linear and rotational kinetic energy in the mean while block of ice just have linear kinetic energy therefore Basketball have more kinetic energy

$K.E = \frac{1}{2}mV^{2}+\frac{1}{2}I^{2} w$  in case of Basket ball

$K.E = \frac{1}{2}mV^{2}$ in case of Ice

b.

For momentum it is obvious that for basketball their is angular momentum along with linear momentum.

P =  m v in case of linear momentum while

L=    I w in case of angular momentum where I have rotational inertia and w is the angular velocity

their is no angular momentum in case of an ice block because it was moving in linear motion.

c.

Due to the additional angular momentum conserved in the case of basketball so it has more energy conserved as compared to ice block therefore frictional effect and ramp sloping does not hurt much motion of basketball as compared to ice blocking.