Work and Kinetic Energy
Answers to Even-numbered Conceptual Questions
Any force acting on an object can do work.
The work done by different forces
may add to produce a greater net work, or they may cancel to some extent.
It follows that
the net work done on an object can be thought of in the following two equivalent ways: (i)
The sum of the works done by each individual force; or (ii) the work done by the net
The tension in the string does no work on the bob, because it always acts at right angles to
the motion of the bob.
Gravity, on the other hand, does negative work on the bob as it
rises, and positive work as it descends.
If the net work done on an object is zero, it follows that its change in kinetic energy is also
Therefore, its speed remains the same.
Frictional forces do negative work whenever they act in a direction that opposes the
For example, friction does negative work when you push a box across the floor,
or when you stop your car.
A car with a speed of
/2 has a kinetic energy that is 1/4 the kinetic energy it has when its
Therefore, the work required to accelerate this car from rest to
Kinetic energy depends on the speed squared; therefore, increasing the speed by a factor
of 3 increases the kinetic energy by a factor of 9.
The fact that the ski boat’s velocity is constant means that its kinetic energy is also
Therefore, the net work done on the boat is zero.
It follows that the net force
acting on the boat does no work.
(In fact, the net force acting on the boat is zero, since its
velocity is constant.)
Kinetic energy depends on both mass and speed; therefore, what the
elephant lacks in speed it can more than make up for in mass.
speed and mass contribute to the kinetic energy.
For example, if the elephant were at rest,
its kinetic energy would be zero – no matter how massive it is.
A moving gazelle will
always have a nonzero kinetic energy.
What we can conclude is that the net force acting on the object is zero.
The work required to stretch a spring depends on the square of the amount of stretch.
Therefore, to stretch a spring by the amount
requires only 1/4 the work required to
stretch it by the amount 2
In this case, the work required is
To stretch this
spring by 3 cm requires 3
= 9 times the work to stretch it 1 cm.
Therefore, stretching to 3
cm requires the work 9
Subtracting from this the work
required to stretch to 2
cm, we find that an addition work of 5
/4 is required to stretch from 2 cm to 3 cm.
Power depends both on the amount of work done by the engine, and the amount of
time during which the work is performed.
If engine 2 does its work in less than half the
time of engine 1, it can produce more power.