1. SECTION 5.3 FORCE AND MOTION IN 2 DIMENSIONS
 Objectives
Determine the force that produces equilibrium when three forces act on an object.
Analyze the motion of an object on an inclined plane with and without friction.

2. INTRO
When Friction acts between 2 surfaces you must take into account both the frictional force that is parallel to the surface and Normal (Perpendicular) to the surface.
Now we will use our skills in adding vectors to analyze situations in which the forces acting on the object are at angles other than 90°.

3. EQUILIBRIUM REVISITED
Recall that when the net force on an object is zero, the object is in equilibrium.
According to Newton’s laws, the object will not accelerate because there is no net force acting on it; an object in equilibrium is motionless or moves with constant velocity.
It is important to realize that equilibrium can occur no matter how many forces act on an object. As long as the resultant is zero, the net force is zero and the object is in equilibrium.
Go over Figure 5-11 p. 131

4. EQUILIBRIUM REVISITED
Resultant Force – vector sum of 2 or more vectors.
Equilibrium – condition in which net force on an object is zero. When the net force is zero the object is in equilibrium.
Equilibrant Force – force needed to bring an object into equilibrium. Force that is applied to produce equilibrium. We will use this for the lab. It is the single additional force that if applied to the same point as the other forces, will produce equilibrium.
To find the equilibrant find the Resultant Force. The equilibrant force is equal in magnitude to the resultant but opposite in direction. So add 180°.
Go over Figure 5.12 p. 131

5. MOTION ALONG AN INCLINED PLANE
From the old book.
***** F = Fg cos 
***** F|| = Fg sin 
When the incline becomes steeper F|| becomes greater and F becomes smaller.
The inclined plane exerts an upward force perpendicular to its surface, this is the NORMAL FORCE.
Since the trunk has no acceleration perpendicular to the plane all forces in that direction must balance. Therefore we get the following equations.
FN + F = 0
FN – Fg cos  = 0
FN = Fg cos 

6. MOTION ALONG AN INCLINED PLANE
If there is no friction between the trunk and the plane, the only force on the trunk is the parallel component of its weight and F|| = Fg sin . So then according to Newton’s 2nd Law the acceleration would be
a = F / m = Fg sin  / m
But Fg / m = g so the acceleration can be found using
***** a = g sin 
And if there is friction then we get
***** a = g(sin  - μ cos )

7. MOTION ALONG AN INCLINED PLANE
Do Example Problem 5 p. 133
F = Fg cos  F|| = Fg sin 
F = 562 cos 30° F|| = 562 sin 30°
F = N F|| = 281 N
Do Practice Problems p. 133 # 33-37

8. MOTION ALONG AN INCLINED PLANE
Do Example Problem 6 p. 134
Fg = mg F = Fg cos  F|| = Fg sin 
Fg = 62(9.8) F = cos 37° F|| = sin 37°
Fg = N F = N F|| = N
Then
FF = μFN FNet = F|| - FF vF = vI + at
FF = .15(485.25) ma = – vF = (5)
FF = N 62a = vF = 23.6 m/s
a = 4.72 m/s2

9. MOTION ALONG AN INCLINED PLANEOR
a = g(sin  - μ cos ) vF = vI + at
a = 9.8(sin 37° (cos 37°)) vF = (5)
a = 9.8(.482) vF = 23.6 m/s
a = 4.72 m/s2
Do Practice Problems p. 135 # 38-41
Do 5.3 Section Review p. 135 # (Skip 42, 45, 46)