Chapter 12, Problem 30A

Jim says that in race between a can of water and a can of ice rolling down an incline, the water filled can will win because the water inside ’slides' down the incline, while the ice is made to rotate, slowing its movement down the incline. John now agrees. Do you agree?

To determine

The one that will win in a race between a can of water and a can of ice rolling down an incline.

Answer to Problem 30A

A can of water will roll down faster than a can of ice.

Explanation of Solution

Introduction: An object in its liquid phase has low viscosity and lesser rotational inertia as compared to the object in its solid phase.

A can of liquid flowing down an incline consists of thin particles that possess low viscosity and due to lesser rotational inertia, angular velocity increases. Gravitational force does the rest of the work. This all helps it to flow or slide down inside the can and can roll faster.

However, in a can of ice, thick particles create more viscosity. Also, ice will have to distribute its potential energy into translational energy and rotational energy to roll down an incline. Due to which more rotational inertia exerts lesser angular velocity. Now, even if the gravity acting upon both the cans is the same. Still, internal forces slowdown in rolling down the incline. This decrease in speed makes the can of water winner.

Conclusion: The can of water will roll down faster.