121
(1)(2)
Example: forces in perpendicular directions on the same object
Question: An object is initially at rest. Two constant forces begin
acting on it, and continue acting on it for a while. As suggested
by the two arrows, the forces are perpendicular, and the right-
ward force is stronger. What happens.
Answer: Aristotle believed, and many students still do, that only
one force can �give orders� to an object at one time. They
therefore think that the object will begin speeding up and moving
in the direction of the stronger force. In fact the object will move
along a diagonal. In the example shown in the figure, the object
will respond to the large rightward force with a large acceleration
component to the right, and the small upward force will give it a
small acceleration component upward. The stronger force does
not overwhelm the weaker force, or have any effect on the
upward motion at all. The force components simply add together:
=0
F
x,total
=F
1,x
+F
2,x
=0
F
y,total
=F
1,y
+F
2,y
Discussion Question
The figure shows two trajectories, made by splicing together lines and circular
arcs, which are unphysical for an object that is only being acted on by gravity.
Prove that they are impossible based on Newton�s laws.
F
1
F
2
direction
of motion
x
y
Section 6.3Newton�s Laws in Three Dimensions