Can a Small Force Reverse the Direction of a Moving Train?

In summary, Newton's 2nd law states that the rate of change of momentum is proportional to the resultant force and in the same direction. If a train of 1000 tonnes is moving with constant velocity on a rough surface, applying a small force in the opposite direction may not immediately reverse its direction. This is because a large force or a small one for a long time is needed to change the momentum from positive to negative.
  • #1
rohanprabhu
414
2
Newton's [itex]2^{nd}[/itex] law states that:

The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

Let us assume that a train of 1000 tonnes is moving with a constant velocity [so, [itex]\frac{dp}{dt} = 0[/itex] (p = momentum)] on a rough surface in the [itex]\hat{i}[/itex] direction.

Now, i apply a small force, of a very small magnitude, in the [itex]- \hat{i}[/itex] direction i.e. in the opposite direction of the motion. Will it cause the train's direction to reverse? Here, the force applied by the engine is just enough to counteract the force due to friction. So, even a small force [which i can myself] apply on the train, can i reverse the direction of the train?

I'm asking this because it seems quite like a paradox to me. The 1000 tonnes figure is more or less for the perceptual impact :D.
 
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  • #2
The rate of change of the momentum would be the the -i direction (for as long as the force is applied), but the momentum itself would still be in the +i direction, until the momentum reaches zero. Therefore you would either need to apply a very large force, or apply a small force for a very long time to actually reverse the direction of the train.
 
  • #3
While you may be making the net force on the train point in the opposite direction as its motion, that doesn't mean it'll instantly reverse direction. To change the large (let's say) positive velocity to a negative velocity will take a large acceleration or a small one for a long time (as nicksauce said).
 

1. What is force?

Force is a physical quantity that describes the push or pull applied to an object. It is measured in units of Newtons (N).

2. What are the different types of forces?

There are four fundamental types of forces: gravitational, electromagnetic, weak nuclear, and strong nuclear. Other types of forces include friction, tension, and normal force.

3. How is force related to motion?

According to Newton's first law of motion, an object will remain at rest or in motion with a constant speed and direction unless acted upon by an external force. In other words, force is necessary to change the motion of an object.

4. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Velocity takes into account both the speed and direction of motion.

5. How is the direction of motion affected by force?

The direction of motion is affected by the direction of the applied force. If the force is applied in the same direction as the motion, the speed of the object will increase. If the force is applied in the opposite direction, the speed of the object will decrease. If the force is applied at an angle, the motion of the object will change direction accordingly.

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