Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

PROBLEMS AND EXAMPLE 53

y

x

1

1

FIGURE 3.8 C=Diagonal alongx=1toy=1.

Problem 3.2

IfF(x,y)=−yandG(x,y)=xy, evaluate the line integral over the quarter-circular

arc fromx=1toy=1 (Fig. 3.9). Notice that the beginning and end points are the

same and the functions are the same as in the previous problem butthe path is

different.

y

x

1

1

FIGURE 3.9 C=Quarter-circular arc.

Problem 3.3

Amassmof 20.0 kg is raised to a heighthof 20.0 m and allowed to drop. Ignoring

air resistance, what is its speed when it hits the ground? What is its kinetic energy?

Problem 3.4

A 20-kg rock was carried up a hill that is 20 m high.

(a) What was the energy increase in the rock?

(b) What amount of work was done on the rock when carrying it up the hill?

(c) What is the kinetic energy gained by the rock when it rolls down the hill?