Page 25 - Fisika Terapan for Engineers and Scientists

Summary 225

DOT PRODUCT (OR SCALAR PRODUCT) A B AB cos u A B A B A B (7.6; 7.8)
x x y y z z
OF TWO VECTORS

WORK DONE BY CONSTANT GRAVITATIONAL W mgh (7.11)
FORCE (Descending from a height h)

WORK DONE BY A VARIABLE FORCE b This area is work done (7.15)
by F x during motion
In one dimension W F (x) dx F x from x = a to x = b.
x
a

x
a b

In two or three dimensions (7.16)
W F # ds

2
2
1
WORK DONE BY A SPRING W k (b a ) (7.17)
2
(Moving from x a to x b)
KINETIC ENERGY 1 2 (7.23)
K mv
2

WORK–ENERGY THEOREM ¢K W (7.25)

GRAVITATIONAL POTENTIAL ENERGY U m g y (7.29)

RELATION BETWEEN WORK AND CHANGE W ¢U (7.31)
IN POTENTIAL ENERGY

MECHANICAL ENERGY E K U (7.34)

CONSERVATION OF MECHANICAL ENERGY E K U [constant] (7.35)

1 2 1 2 y
CONSERVATION OF MECHANICAL ENERGY mv mg y mv mg y 2 (7.37)
1
1
2
2 2
AT TWO POINTS 1 2
2
P 1 F = mv 1 + mgy 1
1 2
F = mv 2 + mgy 2
2
y 1
y 2
O x