Non-central force and work done

In summary, the work done in the case of starting from point O, covering a distance and returning to the same point is zero. For a non-central force as shown in the picture, if the circle it travels along is centered at the origin, the work done will also be zero. The differential d(phi) is used to define the change in angle as the object moves in a circular motion. As the radial force does not change the distance, there is no work done by it. However, the work done by the theta component may not be zero if the angle changes and the object returns to the same point.
  • #1
Samia qureshi
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when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?
que2.jpg
:oldconfused:
 
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  • #2
Samia qureshi said:
when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?

i do not understand your differential d(phi) ; how this is defined...
well you have a force which has two parts radial one F(r) and F(theta) the motion is in a plane (r, theta) so any displacement has two parts ;
as it is moving in a circle r is not changing so no work done by the radial force ...as regards theta part as the angle is changing and it returns to the same point after covering 2.pi angle ...
how come the work done will be zero ...so try to analyse your answer.
 
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  • #3
drvrm said:
i do not understand your differential d(phi) ; how this is defined...
well you have a force which has two parts radial one F(r) and F(theta) the motion is in a plane (r, theta) so any displacement has two parts ;
as it is moving in a circle r is not changing so no work done by the radial force ...as regards theta part as the angle is changing and it returns to the same point after covering 2.pi angle ...
how come the work done will be zero ...so try to analyse your answer.
means if angle changes work done will not b zero? if angle changes and still it returns to same point then will it b zero?
 
  • #4
Samia qureshi said:
when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?
Is the circle that it travels along centered at the origin?
 

FAQ: Non-central force and work done

What is a non-central force?

A non-central force is a type of force that does not act towards a single fixed point. Instead, it acts towards a changing point or in multiple directions. Examples of non-central forces include friction, tension, and air resistance.

How is work done by a non-central force calculated?

The work done by a non-central force is calculated using the formula W = ∫F · ds, where W is the work done, F is the force, and ds is the displacement. This integral takes into account the changing direction of the force and the displacement.

What is the difference between conservative and non-conservative forces?

Conservative forces are those that do not depend on the path taken by an object and only on its initial and final positions. Non-conservative forces, on the other hand, depend on the path taken and may result in a net change in energy of the system.

How does the work-energy theorem apply to non-central forces?

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. This applies to non-central forces as well, as the work done by these forces will result in a change in the object's kinetic energy, even if the force and displacement are not in the same direction.

Can non-central forces do positive or negative work?

Yes, non-central forces can do both positive and negative work. Positive work is done when the force and displacement are in the same direction, resulting in an increase in the object's kinetic energy. Negative work is done when the force and displacement are in opposite directions, resulting in a decrease in the object's kinetic energy.

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