Name
Period
Date
Energy: Worksheet 3
Work and the Dot Product

1. A constant force given by F  3.5 N  iˆ  1.5 N  ˆj is applied to an object of mass

15 kg to move it through a displacement of r  4.0 m  iˆ  3.0 m  ˆj .
a. What are the magnitudes of the force and the displacement? Begin by sketching
a vector diagram for each.
b. What is the angle between the force and the displacement?
c. How much work is done by the force?
Energy: Worksheet 3
page 2

2. Let two vectors be represented in terms of their coordinates as a  a x iˆ  a y ˆj  a z kˆ

 
and b  b iˆ  b ˆj  b kˆ . Show that a  b  a b  a b  a b .
x
y
z
x x
y
y
z
z
3. Using what you just proved in (2), calculate the work done by a force

F  25 N  iˆ  12 N  ˆj  34 N  kˆ that moves an object through a displacement of

r   6.2 m  iˆ  22 m  ˆj  5.0 m  kˆ .
 
4. Use the definition of scalar product a  b  ab cos  and the fact that in problem (2)
 
you proved that a  b  a x bx  a y b y  a z bz to calculate the angle between the force and

the displacement given by F  3.0 N  iˆ  3.0 N  ˆj  3.0 N  kˆ and

r  2.0 m iˆ  1.0 m ˆj  3.0 m kˆ .