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

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?