Question

A ball is sliding from the top to the bottom of a plank without rolling (e.g. imagine the surface is covered in ice, so very slippery). The ball is returned to the top and released again, but this time the ball is rolling (without slipping) down the plank (imagine the ice has melted). Compare the speeds of the ball at the bottom.a.The final speed is the same in both cases.b.The final speed is larger in the second case (with rolling).c.The final speed is larger in the first case (without rolling).d.The final speed is larger in the first case (without rolling) if the the plank is at an angle bigger than 45o and smaller if the angle is less than that.

Answer 1

To find:

Compare the speeds of the ball at the bottom of the plank.

Step-by-step explanation:

From the law of conservation of energy, the total energy of the system always remains constant. Thus the total energy of the ball at the bottom of the plank must be equal to its total energy at the top of the plank.

When the ball is at the top of the plank, the ball has only potential energy. When the ball slides down to the bottom, this potential energy is converted into translational kinetic energy.

The translational kinetic energy is directly proportional to the square of the velocity of the object. Thus when the translational kinetic energy is high the velocity of the ball will be high.

When the ball rolls down the bottom of the plank, the initial potential energy of the ball is converted into translational and rotational kinetic energy.

The rotational kinetic energy of an object is proportional to the square of the angular velocity of the object.

Thus in the first case, the translational kinetic energy and hence the speed of the ball will be larger compared to that in the second case.

Final answer:

Thus the correct answer is option C.