Pushing a trolley (equal and opposite forces)

[SUDOnym]

Hi there

I have been posed a brain teaser:

If pushing against a trolley, if there is an equal and opposite opposing force (ie. friction) why may the trolley still acceleerate?

The best solution I have is that between the wheels and the ground there is a static friction force. This force on the bottom of the wheels causes a torque by R(cross)F so the wheels begin to rotate, pulling the cart along with it... .
... But it still seems a little like a contradiction that something can have a linear acceleration with no net force... .

Anyone care to clarify this?

 

[Doc Al]

If pushing against a trolley, if there is an equal and opposite opposing force (ie. friction) why may the trolley still acceleerate?

Are you sure the poser was talking about equal and opposite forces on the trolley? Often folks are stumped by Newton's 3rd law, which states that if you push against the trolley the trolley will push back against you with an equal and opposite force.

In any case, you are correct: If there is no net force on the trolley, it cannot accelerate.

 

[Whovian]

Basically, the trolley pushes against you with equal and opposite force. You can counter this force by having the ground push against you, caused by you pushing against the ground (push harder to be able to accelerate with the trolley,) and so there's no net force on you (unless you pushed harder,) but there is a net force on the trolley and the ground. So the ground accelerates backwards an insignificant amount, and the trolley accelerates forwards a significant amount.

 

[SUDOnym]

yea... I think that was it actually...

The idea is that the trolley exerts an equal and opposite force on the pusher so how does the pusher go in the direction he wants to go...?
Answer:
The pusher is also pushing against the Earth and so it is the Earth that provides force to the pusher to go in the direction he wants to go... The Earth also feels a torque due to the force the pusher is applying but it is so small as to immeasurable...
Would you have anything to add to my explanation?

 

[pmacias]

Hello there,

It is a common misconception that an object can only accelerate if there is a net force acting on it. However, in the case of the trolley, the equal and opposite forces (pushing and friction) do not cancel each other out completely. This is because friction is a type of force that opposes motion, but it is not always equal to the applied force. In this scenario, the force of friction is less than the applied force, allowing the trolley to accelerate.

Additionally, as you mentioned, there is also a torque force at play due to the static friction between the wheels and the ground. This torque causes the wheels to rotate, pulling the trolley along with it. This rotation adds to the overall acceleration of the trolley, even though there is technically no net force acting on it.

In summary, the trolley is able to accelerate because the forces acting on it (pushing and friction) do not cancel each other out completely, and the added effect of torque from static friction also contributes to its acceleration. I hope this helps clarify the situation for you. Keep exploring and questioning, that's what science is all about!