Inclined Planes

1
Inclined Planes

• ? I LOVE these! ?

2
What Exactly will we be looking at?

• Visualize an object placed on a ramp.
• In physics we refer to the ramp as an inclined
  plane.

• We are still NEGLECTING friction so, if you put
  an object on an inclinewhat will it do?

• Yup! It will slide down the incline.
  But, WHY will it slide down the incline?

3
WHY will it slide down the incline?

• Seems simpleIt moves downhill because of
  gravity.
• If there is no friction (to resist the motion),
  then gravity is allowed to accelerate it down
  the incline.
• The force of gravity IS why it is pulled
  downhillbut there is more to it.

• What is the direction of the gravitational force
  on the box?

4
Look at the Direction of Gravity

• The force of gravity (i.e. weight) ALWAYS acts
  directly down (toward the center of Earth).
• Hang onthe box doesnt move straight down it
  moves down the hill.
• The concept of net force (Fnet) indicates that
  there must be a force acting parallel to the
  motion, that causes it to accelerate down the
  incline.

• What is this parallel force?

5
What is this parallel force?

• Lets say that the incline makes an angle of ?
  with the ground.
• The box pushes down on the incline and the
  incline pushes back on the box.
• The support force that the incline supplies to
  the box is the normal force.
• Remember that the normal force is always
  perpendicular to the surface.

?
Do NOT draw the normal force vertically upwardit
must be perpendicular to the surface!

• We will use the normal force to lay out the rest
  of the picture.

6
Let the normal force help you

• Extend the normal force in the opposite
  direction.
• This force is the component of the weight that is
  perpendicular to the surface.

?

• This still isnt parallel to the motionbut were
  getting there...

7
What is the force down the hill?

• Draw a line PARALLEL to the incline
• This force is the component of the weight that is
  parallel to the surface.
• The parallel force is what causes the pull down
  the hill!

?

• We use Fp to find Fnet
• So how do we find Fp?

8
Focus on the triangles.

• Notice that the inclined plane itself is a right
  triangle.
• Notice that the triangle made up of F?, Fp and mg
  is also a right triangle.
• These two triangles are similar triangles.

?

• How does it help us that these two triangles are
  similar?

9
How does it help us that these two triangles are
similar?

• The base angle of the inclined plane (?) is the
  same as the angle between F? and mg.
• You also want to pay attention to where the right
  angle is.

?
?

• You now have the picture you need to analyze the
  situation.

10
What do we do now?

• Lets do a problem! ?
• A block is released (from rest) from the top of
  an incline that makes an angle of 30? with the
  ground. Neglecting friction, what is the
  acceleration of the block down the incline?

30

• Visualize the forces acting on the box as well as
  the direction of the acceleration.

11
What do we do now?

• If the block is going to move down the incline
  there must be a force directed PARALLEL to that
  motion.
• We now know that we need to break the weight (mg)
  up into parallel and perpendicular components.

• The parallel component (Fp mgsin30?) is (part
  of) the net force.

12
What do we do now?

• Fnet maThe net force includes all forces (or
  components of forces that are parallel to the
  motion)
• Fp ma
• mgsin30? ma
• To solve for the acceleration divide both sides
  by mass.
• mgsin30? a m
• gsin30? a
• (9.8)sin30? a 4.9m/s2

Thats it KNOW HOW TO SET UP THE DIAGRAM!
UNDERSTAND HOW TO WORK WITH Fnet!
13
What if we push the box?

• A 5-kg block is pushed up an incline via a
  force of 30N as shown. If the incline makes an
  angle of 30? with the ground and friction is
  neglected, what is the acceleration of the
  block?

30

• Visualize the forces acting on the box as well as
  the direction of the acceleration.

14
What if we push the box?

• Dont forget about the weight (straight down) and
  the normal force (perpendicular to the surface
  and upward).
• Dont forget to break the weight (i.e. force of
  gravity) into components that are parallel to and
  perpendicular to the incline.

F? mgcos30?
30
Fp mgsin30?

• Now you are ready.

15
What if we push the box?

• Fnet maThe net force includes all forces (or
  components of forces that are parallel to the
  motion)
• F - Fp ma
• F is positive b/c it is in the same direction as
  the motion and Fp is negative b/c it is in the
  opposite direction of the motion.
• F - mgsin30? ma
• To solve for the acceleration divide both sides
  by mass.
• F - mgsin30? a m
• 30 (5)(9.8)sin30? a 1.1m/s2
• 5

Fp mgsin30?
Thats it KNOW HOW TO SET UP THE DIAGRAM!
UNDERSTAND HOW TO WORK WITH Fnet!
16
Got it?

• Try it on your own
• BUT
• remember you have lots of support.
• We will do this in class together.
• Use Mrs. McGraths pencast for help
• See the notes on the back of handout 4-5 for help
• ASK QUESTIONS!