Question

Question: A basketball rolls across a classroom floor without slipping, with its centre of mass moving at a certain speed. A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line. Which object has more (i) kinetic energy and (ii) momentum? (a) The basketball does. (b) The ice does. (c) The two quantities are equal. (iii) The two objects encounter a ramp sloping upward. Which object will travel farther up the ramp? (a) The basketball will. (b) The ice will. (c) They will travel equally far up the ramp.

Short answer

Answer

(i) The basketball has more kinetic energy. Hence option(a) is correct.

(ii) Basketball and block of ice, both will have equal momentum. Hence option(c) is correct.

(iii) The basketball will travel farther up the ramp. Hence option(a) is correct.

Step-by-step solution

Defining kinetic energy and potential energy

The energy of an object that it possesses due to its motion is known as kinetic energy. Kinetic energy is equal to half of an objects mass multiplied by the velocity squared.

$\mathit{K}\mathbf{.}\mathit{E}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

The stored energy of an object that it possesses due to the relative position of various parts of a system is known as potential energy. The formula to calculate the potential energy is as follows:

P.E = mgh

Here, m = mass of an object

g =acceleration due to gravity and

h = height.

Explanation for the correct options

The basketball-Earth system has more kinetic energy than the Ice-Earth system due to the rotational kinetic energy of the basketball. Therefore, when the kinetic energy of both the system has transformed to the gravitational potential energy, then the objects momentarily come to rest at their highest point on the ramp, and the basketball will be at higher position corresponding to the larger gravitational potential energy.

Also, the basketball has both rotational as well as translational kinetic energy. The motions of the centres of mass of the two systems are identical. Hence, their momentum will be equal.