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Set 3 Problem number 26
As the total nongravitational
force on an object of mass 3.2 kg does 57 J of work, its gravitational PE also decreases by
82 J. What is its change in KE?
PE decreases when altitude decreases, so that work is done on the object by
gravity. The work done on the object against the net force will tend to increase its
KE.
- As its gravitational PE decreases by 82 J, gravity does 82 J of work ON the object,
which is equivalent to negative work being done BY the object .
- At the same time 57 J of work is done ON the object by all other forces, equivalent to
the - 57 J of work done BY the object against those forces.
- Thus the object does - 57 J - 82 J = -139 J of work against all of the forces acting on
it--i.e., against the net force on it. This is the net work done BY the object.
- As the object does negative work its KE change is equal to the negative of the work done
BY the object, so KE change is --139 J = 139 J.
As an example consider an object falling under the influence of gravity.
- Its gravitational PE decreases, tending to increase its KE.
- If the object is subject to an additional downward force whose magnitude is greater than
that of the air resistance, the net nongravitational force will be in the direction of
motion.
- Work in addition to the work done by gravity is therefore done on the object by the
nongravitational force, tending to further increase its KE.
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