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Set 3 Problem number 25
As an object of mass 6.7 kg does
66 J of work against the net nongravitational force, its gravitational PE also decreases
by 74 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 on it will tend to
increase its KE.
- As its gravitational PE decreases by 74 J, gravity does 74 J of work on the object,
which is equivalent to the object doing negative work.
- At the same time the object does 66 J of work against all other forces.
- Thus the object does 66 J - 74 J = -8 J of work against all of the forces acting on
it--i.e., against the net force on it.
- If an object does positive work against all forces acting on it its KE must decrease,
whereas if all the forces acting on it do positive work on the object (equivalent to the
object doing negative work against the net force) its KE must increase.
- In this case the object does negative work and its KE increases by --8 J = 8 J.
As an example consider an object falling under the influence of gravity.
- Its gravitational PE decreases, tending to increase its KE.
- The object also generally encounters air resistance against which it exerts an equal and
opposite force in its direction of motion. It therefore does work against the air
resistance, which tends to decrease its KE.
- The increase in KE is the difference between the decrease in gravitational PE and the
work done against air resistance.
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