Initial acceleration problem: Two children on a frictionless floor

[Davidmb19]

Homework Statement

A girl of the mass 30kg and a boy of the mass 45kg sit on a frictionless floor holding two ends of a rope. The boy pulls on the rope. The girl moves towards the boy with an initial acceleration of 3ms^-2.
The boy
A. Moves towards the girl with an initial greater acceleration greater than 3ms^-2.
B. Moves towards the girl with an initial acceleration than less 3ms^-2
C) Moves towards the girl with an initial acceleration of 3ms^-2
D) Remains stationary

Homework Equations

The Attempt at a Solution

I thought it would be D the answer is B. I thought this due real life experience; I didn't really think of the physics.

 

[BvU]

Point is you don't have real life experience with a frictionless floor. The closest you come is e.g. on ice.
An experience that would also come close: if both are on an inflated mattress in a pool or something. The physics of action = -reaction is always there; if you can't hold on to something (as is the case on a frictionless floor), then you'll accelerate too.

 

[ehild]

You should think of Physics of that ideal situation: the floor is frictionless. It is not in real life. But you have to solve the given problem.
If there is no friction, is there any external horizontal force? Without force, what is conserved?

Oh, BVU was faster...

 

[Davidmb19]

You should think of Physics of that ideal situation: the floor is frictionless. It is not in real life. But you have to solve the given problem.
If there is no friction, is there any external horizontal force? Without force, what is conserved?

I understand. I didn't think of the momentum if that's what you're implying? Thanks

 

[ehild]

I didn't think of the momentum if that's what you're implying?

Yes, it is.

 

[haruspex]

Point is you don't have real life experience with a frictionless floor. The closest you come is e.g. on ice.
An experience that would also come close: if both are on an inflated mattress in a pool or something. The physics of action = -reaction is always there; if you can't hold on to something (as is the case on a frictionless floor), then you'll accelerate too.

To elaborate on that, if instead you suppose some small coefficient of friction, same for each, then the boy, being heavier, can enjoy a greater frictional force. If the tension in the rope exceeds the girl's friction but not the boy's, only the girl will move.
Lots of questions say "frictionless floor", but in most cases you can read that as merely meaning very low friction and it doesn't significantly change the answer; here it does. So I regard the question as unhelpful in developing students' insight. Waterborne or free fall would have been better contexts.

 

[Rashid-47]

Homework Statement

A girl of the mass 30kg and a boy of the mass 45kg sit on a frictionless floor holding two ends of a rope. The boy pulls on the rope. The girl moves towards the boy with an initial acceleration of 3ms^-2.
The boy
A. Moves towards the girl with an initial greater acceleration greater than 3ms^-2.
B. Moves towards the girl with an initial acceleration than less 3ms^-2
C) Moves towards the girl with an initial acceleration of 3ms^-2
D) Remains stationary

Homework Equations

The Attempt at a Solution

I thought it would be D the answer is B. I thought this due real life experience; I didn't really think of the physics.

According to Newton's 3rd law, the boy is experiencing the same force but the mass of the boy is more so acceleration will be less (a = F/m). That's why the option is B.

 

[haruspex]

According to Newton's 3rd law, the boy is experiencing the same force but the mass of the boy is more so acceleration will be less (a = F/m). That's why the option is B.

Yes.