# Concept of Work Done [closed]

If one of the forces acting on a particle is conservative, will its work equals the change in Kinetic Energy? True or False

Well, according to the formula $\text{W} = \Delta\text{K.E}$ the statement must be true. Any force acting on the particle which produces a change in its kinetic energy does some work and according to the Work-Energy theorem, they should be equal.

So, according to me, the statement must be true. But the answer given in my book says its false.

Can anybody explain why?

## closed as unclear what you're asking by John Rennie, sammy gerbil, stafusa, Emilio Pisanty, Jon CusterNov 13 '17 at 15:45

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• The work done on the particle will be equal to the change in its total energy i.e. kinetic energy + potential energy – John Rennie Nov 12 '17 at 5:51
• @JohnRennie vote to reopen, OP has substantially improved the question – Alex Robinson Mar 16 '18 at 10:12

There's a surprising lack of clarity from the answers here. According to the work-energy theorem, the total work done on an object is equal to its change in kinetic energy.

Additionally, if one of the forces acting on the object is conservative, then the work done by that force is equal to minus the change in the associated potential energy.

These cases are not mutually exclusive. If an object falls a distance $h$ under the influence of gravity alone, then

1. The total work, $W=mgh$, is equal to the change in the object's kinetic energy
2. The work done by gravity, which is also equal to $mgh$, is minus the object's change in gravitational potential energy.

The reason your answer was marked wrong is because it is only the total work which is equal to the change in kinetic energy. If more than one force is acting on the object throughout its motion, then you have to add their contributions.

Concervative force means the work done against it is independand of path. For example gravitational force is concervative ,and you can put a body on the ground to a height h through many paths. But the net gain in energy is mgh. Here kinetic energy is not ever mentioned. so concervative force is not to be sticked with kinetic energy. And generally work done on a system will be used to change potential energy or kinetic energy or both simultaneously

Not necessary. The particle can change shape, or gain height, or the force can counteract an existing force(for example hovering it).