Page 59 - Fisika Terapan for Engineers and Scientists

Summary 259

SUMMARY

PROBLEM-SOLVING TECHNIQUES Energy Conservation (page 238)

PHYSICS IN PRACTICE Hydroelectric Pumped Storage (page 242)

CONSERVATIVE FORCE The work done by the
force is zero for any round trip.

WORK DONE BY A CONSERVATIVE FORCE W U U ¢U (8.2)
2 1

1
POTENTIAL ENERGY OF A SPRING U k x 2 U (x) (8.6)
2

x

CONTRIBUTIONS TO THE MECHANICAL ENERGY
2
1
Kinetic energy K mv (for motion)
2
Gravitational potential energy U mgy (near Earth’s surface)
1
2
Elastic potential energy U kx (for a spring)
2
x
POTENTIAL ENERGY AS INTEGRAL OF FORCE U (x) F (x ) dx (8.14)
x
x 0
A A
POTENTIAL OF INVERSE-SQUARE FORCE If F (x) 2 then U (x) (8.19)
x x
(for x 0; attractive for A 0, repulsive for A 0.)

dU U For repulsive U
FORCE AS DERIVATIVE OF POTENTIAL ENERGY F force, dU/dx x (8.21)
x
dx is negative.
For attractive
force, dU/dx
x
is positive.
2
1
CONSERVATION OF MECHANICAL ENERGY E mv U [constant] U (8.17)
2
Turning points
x
0
E
Energy level

MASS IS A FORM OF ENERGY E mc 2 (8.30)

ENERGY HAS MASS ¢m ¢E (8.32)
c 2