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Question

To pull a wagon across a lawn at a constant velocity you must exert a steady force. Reconcile this fact with Newtons first law which states that motion with a constant velocity indicates no force

Answer 1

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Following is the answer to your question.

As per Newton's law of motion wagon with constnant velocity implies no force acts on it.

However if we apply a force , we are not applying the force to make it move with constant velocity but to cancel some other external force that may otherwise act on the body.

There is always a force called friction which we cannot make to zero unless we apply a force.
However we can reduce the friction and apply a small force to make the net force to zero.

In a high friction floor objects once set into motion soon comes to rest.

But if there is less amount of friction , that is smooth floor, objects which were set into motion and left free, goes on moving through a long distance before coming to rest.

In an ideal floor where there is no friction objects which are set into motion will continue to move with constant uniform speed maintaining its direction also in a straight line and will never come to rest unless a force acts on it.

In the case of lawn and wagon, the floor is exerting a frictional force in the opposite direction of the motion of the wagon.

To make the net force on the wagon equal to zero, we apply equal and opposite force to the frictional force.

The net force on the wagon is now zero and the wagon moves with constant velocity ( constnat speed and in straight line).

If the applied force is increased even by a small amount then the wagon's speed will be increasing continuosly and there will be no limit for the increase of the speed as long as the constnat force acts on it.

If the force is reduced even by a small amount then the frictional force will be more than the applied force and the wagon's speed continoulsly decreases and eventually comes to rest.

Answer 2

The force that you apply to bring the wagon into motion from position of rest has to be more than the force of friction applied by the lawn. As it starts to move with uniform velocity the applied force just cancels the frictional force and net force on the wagon is zero hence acceleration is zero. That is Newton's first law!

Answer 3

This sounds like a homework problem, which you should be researching for yourself. A little hint, think about friction, which is already exerting a force...