Simple Nature - Light and Matter

F > 0 dx > 0 dK > 0

F < 0 dx < 0 dK > 0

F > 0 dx < 0 dK < 0

F < 0 dx > 0 dK < 0

This looks exactly like the rule for determining the sign of a product,
and we can easily show using the chain rule that this is indeed a
multiplicative relationship:

dK=

dK

dv

dv

dt

dt

dx

dx [chain rule]

= (mv)(a)(1/v) dx

=madx

=F dx [Newton’s second law]

We can verify that force multiplied by distance has units of energy:

N·m =

kg·m/s

s

×m

= kg·m^2 /s^2

= J

A TV picture tube example 30

.At the back of a typical TV’s picture tube, electrical forces accel-

erate each electron to an energy of 5× 10 −^16 J over a distance

of about 1 cm. How much force is applied to a single electron?

(Assume the force is constant.) What is the corresponding accel-

eration?

.Integrating

dK=Fdx,

we find

Kf−Ki=F(xf−xi)

or

∆K=F∆x.

The force is

F=∆K/∆x

=

5 × 10 −^16 J

0.01 m

= 5× 10 −^14 N.

Section 3.2 Force in one dimension 165