Energy transfer

a car moving in a circular path? (a) the car

has tangential acceleration but no centripetal acceleration. (b) the car has centripetal acceleration but no tangential acceleration. (c) the car has both centripetal acceleration and tangential acceleration.

Quick Quiz 1 If a fly collides with the windshield of a fast-moving bus, which object experiences an impact force with a larger magnitude? (a) the fly (b) the bus (c) the same force is experienced by both.

Quick Quiz 2 In a free-body diagram for a single object, you draw (a) the forces acting on the object and the forces the object exerts on other objects, or
(b) only the forces acting on the object.

Energy.

pushed along a chalkboard tray.

the action of a constant force F, the work done

by the force is F∆rcosθ.

The work W done on a system by an agent exerting a constant force on the system is the product of the magnitude F of the force, the magnitude ∆ r of the displacement of the point of application of the force, and cos θ, where θ is the angle between the force and displacement vectors:

(6.1)

horizontal surface, the normal force n and the gravitational force

mg do no work on the object. In the situation shown here, F is the only force doing work on the object.

Work is a scalar quantity, and its units are force multiplied by length. Therefore, the SI unit of work is the newton· meter (N·m). This combination of units is used so frequently that it has been given a name of its own: the joule ( J).

to note that work is an energy transfer. If W

is the work done on a system and W is positive, energy is transferred to the system; if W is negative, energy is transferred from the system. Thus, if a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundary. This will result in a change in the energy stored in the system.

by the force

the varying force as the particle moves from xi to

xf is exactly equal to the area under this curve.

(6.2)

(6.3)

undergoing a displacement ∆r=∆xˆi and a change in velocity under

the action of a constant net force ƩF.

(6.4)

is at x = xi and vf is its speed

at xf.

units as work.
(6.6)
(6.7)
Equation 6.7 is an important result known as

the work–kinetic energy theorem:

In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system.

the block by work; (b) energy leaves the radio from

the speaker by mechanical waves; (c) energy transfers up the handle of the spoon by heat.

gas tank by matter transfer; (e) energy enters the hair

dryer by electrical transmission; and (f) energy leaves the light bulb by electromagnetic radiation.

(d)

(e)

(f)

the notion that we can neither create nor destroy energy—energy

is always conserved. Thus, if the total amount of energy in a system changes, it can only be due to the fact that energy has crossed the boundary of the system by a transfer mechanism such as one of the methods listed above. This is a general statement of the principle of conservation of energy. We can describe this idea mathematically as follows:

(6.8)

an external force is applied to an object (which we

assume acts as a particle), and if the work done by this force in the time interval ∆t is W, then the average power during this interval is defined as

definition of velocity and acceleration, we define the instantaneous power

as the limiting value of the average
power as ∆t approaches zero:

(6.9)

transfer. Therefore, the most general expression for power is
The SI

unit of power is joules per second ( J/s), also called the watt (W) (after James Watt):

A unit of power in the U.S. customary system is the horsepower (hp):

(6.10)

an external agent on the system of the book and

the Earth as the book is lifted from a height ya to a height yb is equal to mgyb - mgya.

(6.11)

the gravitational force on the book as the book falls

from yb to a height ya is equal to mgyb - mgya.

the book,
Now, let us relate each side of this equation

to the system of the book and the Earth. For the right-hand side,

(6.12)

(6.13)

(6.14)

mechanical energy:
We will encounter other types of potential energy besides

gravitational later in the text, so we can write the general form of the definition for mechanical energy without a subscript on U:

(6.15)

(6.16)

(6.17)

for an isolated system. An isolated system is one for

which there are no energy transfers across the boundary. The energy in such a system is conserved—the sum of the kinetic and potential energies remains constant.

(6.18)

by a conservative force on a particle moving between any

two points is independent of the path taken by the particle.
2. The work done by a conservative force on a particle moving through any closed path is zero. (A closed path is one in which the beginning and end points are identical.)

properties 1 and 2 for conservative forces. Nonconservative forces acting

within a system cause a change in the mechanical energy Emech of the system. We have defined mechanical energy as the sum of the kinetic and all potential energies.

on an object within a system equals the negative derivative

of the potential energy of the system with respect to x.

Relationship Between Conservative Forces
and Potential Energy

across a horizontal surface with an initial speed v. It

slides until it stops due to the friction force between the block and the surface. The same block is now projected across the horizontal surface with an initial speed 2v. When the block has come to rest, how does the distance from the projection point compare to that in the first case? (a) It is the same. (b) It is twice as large. (c) It is four times as large. (d) The relationship cannot be determined.

Quick Quiz 2