Inclined Planes

1
Inclined Planes

• Label the direction of N and mg.

N
mg
?
Use slide show mode (press F5) for animations.
2
Inclined Planes

• Mark the direction of acceleration a.

N
a
mg
?
3
Inclined Planes

• Choose the coordinate system with x in the same
  or opposite direction of acceleration and y
  perpendicular to x.

y
N
x
a
mg
?
4
Inclined Planes

• Now some trigonometry

y
N
x
a
?
90- ?
mg
?
5
Inclined Planes

• Replace the force of gravity with its components.

y
N
x
a
mg sin?
mg cos?
?
mg
?
6
Inclined Planes

• Use Newtons second law for both the x and y
  directions

y
N
x
a
mg sin?
mg cos?
?
mg
?
The force and acceleration in the x-direction
have a negative sign because they point in the
negative x-direction.
7
Inclined Planes

• Why is the component of mg along the x-axis
  mgsin?
• Why is the component of mg along the y-axis
  mgcos?

8
Inclined Planes

• Why is the component of mg along the x-axis
  mgsin?
• Why is the component of mg along the y-axis
  mgcos?

y
N
a
mg sin?
x
?
?
mg
mg cos?
9
Inclined Planes

• Why is the component of mg along the x-axis
  mgsin?
• Why is the component of mg along the y-axis
  mgcos?

y
N
a
mg sin?
x
?
mg
mg cos?
10
Inclined Planes

• Why is the component of mg along the x-axis
  mgsin?
• Why is the component of mg along the y-axis
  mgcos?

y
opposite
N
sin?
a
hypotenuse
adjacent
cos?
mg sin?
hypotenuse
x
?
mg
mg cos?