Download Forces in Equilibrium & Motion along an Incline

Forces in Equilibrium &
Motion along an Incline
Chapter 7.1
Equilibrium
Newton’s 1st Law of Motion



When the forces on an object are balance,
it is said to be in equilibrium.
When an object is in equilibrium, it is not
accelerating.
An object that is not accelerating is
stationary or moving at constant speed in a
straight line.
You balanced forces during the force table lab.
Ex. 1: Equilibrium
A 100 N sign is hung by two wires as seen
below. What is the tension in the wires?
FB
FA

 = 15°

Physics is Fun
Fg = 100 N
Diagram the Problem
y
FA

FB
x

Physics is Fun
System
Fg = 100 N
y
FAx
FAy
FBx
FA
FB


 = 15°
Fg = 100 N
FBy
x
State the Known & Unknown
What is known?


Fg = 100N
θ = 15°
What is not known?


FA
FB
Perform Calculations
Isolate the x and y components separately.
Since the sign is not moving, Fnet = ma = 0 in both the x
and y directions.
x – direction:



-FAx + FBx = 0
-FA cosθ + FB cosθ = 0
FA cosθ = FB cosθ
y – direction:




FA sinθ + FB sinθ – Fg = 0
2FA sinθ = Fg
FA = (100N)/(sin(15°)(2)
FA = 193 N
Motion on an Incline
When objects are not on a
flat level surface:


A portion of the
gravitational force is directed
along the surface.
The normal force is not
equal to the weight of the
object.
Choose a coordinate
system such that the x-axis
is directed parallel to the
slope.
FN
Fgx
F
g
Fgy
Ex. 2: Motion on an Incline
Determine the rate of acceleration of
a 25 kg wooden crate as it slides
down a wooden ramp with a
coefficient of friction,  = 0.2. The
angle the ramp makes with the
horizontal is 30.
What is known?




m = 25 kg
 = 0.2
θ = 30
vi = 0 m/s
System
FN
Fgx

What is not known?

a=?
F
g
Fgy
Diagram and Solve the
Problem
y-axis
y-direction:



x-axis
Fnet,y = FN – Fgy
Since Fnet,y = 0
FN = Fgy = mgcosθ
FN
Fnet,x = Fgx – Ff
ma = mgsinθ – μFN
ma = mgsinθ - μmgcosθ
a = g(sinθ – μcosθ)
a = 9.8 m/s2(sin 30° - μcos 30°)
a = 3.2 m/s2
Fg(x)
x-direction:






Ff


Fg(y)
Fg
Key Ideas
Equilibrium:

When an object is at rest, or when an object
is in motion at a constant speed in a straight
line.