Can a Sphere Roll Without Slipping on a Frictionless Surface?

[Saitama]

Homework Statement

A solid sphere of mass M and radius 1m rests on a smooth horizontal surface. A force F acts on sphere as shown in figure. If it rolls without slipping, find the value of H.

Homework Equations

The Attempt at a Solution

This problem was presented by the teacher today.

My question is, how it can start rolling without slipping in absence of friction?

The teacher solved the problem in the following way:

Torque about CM: FH=Iα or α=(5/2)(FH/M).
From Newton's second law: F=Ma or a=F/M.
From the condition of rolling without slipping a=α (radius is 1 m as per the question)

Hence, H=(2/5) metres.

But this doesn't make sense, I have read that friction is required to initiate rolling. In absence of friction, an impulse can be provided at a suitable height to start rolling but in the given question, a force is applied.

Any help is appreciated. Thanks!

 

[rcgldr]

As long as the force is applied, the sphere will experience linear and angular acceleration. With the proper value of H, the sphere will "roll" as it accelerates, meaning it's surface speed relative to the center of mass will equal the linear speed of the sphere.

 

[haruspex]

I have read that friction is required to initiate rolling.

That's a popular myth. As rcgldr says, rolling merely means that there is no relative motion of the surfaces in contact. Friction is the usual way for that state to be achieved, but it is not the only way.

 

[Saitama]

Thank you very much rcgldr and haruspex.

 

[Nickie]

I would first clarify with the teacher how they defined "rolling without slipping" in this context. It is possible that they are using a simplified model that assumes ideal conditions, where there is no friction present at all. In this case, the force F would be enough to initiate rolling without slipping, as there would be no opposing force from friction to prevent it from rolling.

However, in reality, friction is present in most situations and is necessary for an object to start rolling. Without friction, the object would simply slide instead of rolling. So, if this is a real-world scenario, the solution provided by the teacher may not accurately reflect what would happen in practice.

I would also consider the limitations of the model being used and the assumptions being made. It is important to carefully consider all factors and variables in a situation before drawing conclusions or making predictions.