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Chapter 5: Lesson 4 - Inclined Planes
Chapter 5: Lesson 4 - Inclined Planes
Equations
Equations
We are going to expand our available math equations in this lesson. It will be helpful to have your equation sheet ready. A copy of the equation sheet is under resource materials on this website and on google classroom. It can also be found HERE.
Inclined Planes
Inclined Planes
An object placed on a tilted surface will often slide down the surface. The rate at which the object slides down the surface is dependent upon how tilted the surface is. The greater the tilt of the surface, the faster the rate at which the object will slide down it.
In physics, a tilted surface is called an incline plane. Objects are known to accelerate down an incline plane because of an unbalanced force.
Forces on an inclined plane
Forces on an inclined plane
There are always at least two forces acting upon any object that is positioned on an inclined plane. A gravitational force and the normal force.
The gravitational force, or weight, acts in a downward direction.
Normal Forces
Normal Forces
In chapter 4, all of our surfaces were horizontal, so the normal force always pointed up, opposite the direction to the gravitational force.
Normal forces always are directed perpendicular to the surface that they are sitting on. Now that our surface is tilting, that is a very important piece to remember!
Components of the Gravitational Force
Components of the Gravitational Force
When an object is sitting on an inclined plane the gravitational force doesn't tell us much about what is happening with the object. It would be better to resolve that gravitational force vector into two components (remember chapter 5, lesson 2 on vector resolution) a component that is parallel to the incline plane and a component perpendicular to the incline plane. Looking at the picture, you can see that the gravitational force, in black, was resolved into two other components, F|| for the parallel force and F⟂ for the perpendicular force.
Net Force
Net Force
The perpendicular component of the force of gravity is directed opposite to the normal force. They balance each other out. The net force is that direction is zero. When you find the perpendicular force, you know that that value is the same as the normal force.
The parallel component of the gravitational force is not balanced out by any other force. The object will accelerate down the incline plane due to the presence of an unbalanced force. It is the parallel component of the force of gravity which causes this acceleration.
What happens when the Inclined Plane gets steeper or less steep?
What happens when the Inclined Plane gets steeper or less steep?
Click on the video to see an explanation to what will happen to the parallel and perpendicular components when the angle of the inclined plane increases or decreases.
Calculating the Parallel and Perpendicular Components of the Gravitational Force
Calculating the Parallel and Perpendicular Components of the Gravitational Force
From watching the video, you saw that the equations for the parallel and the perpendicular components of the gravitational force are
F|| = mg * sin θ
F⟂= mg * cos θ
If you are given a mass in the problem, you can substitute the mass for m and then multiply by g. If you are given a force in the problem, you have to remember that F=mg and you can just substitute the force both (mg). Do not multiply the force by gravity in these equations. Your answer will be off by a factor of 10.
Math
Math
Click here to see the paper that I used in the video.
As you watch this video, pause it and try the math on your own. When you have your answer, start the video and see if you are right. It is important to know where YOU make your mistakes so you can correct them for next time!
Remember there are more practice math problems under Chapter 5 Resources. Practice the math and see if your answer matches my answer.
Check Your Understanding:
Check Your Understanding:
Click on the down arrow when you have your answer to check to see if you are correct.
Look at the picture. The weight of the box is 100 N and is sitting on a 30º inclined plane. What is the parallel and the perpendicular component to the gravitational force?
F=100 N
θ=30 degrees
F|| = ?
F⟂= ?
Remember F=mg, so since we have a Force, you can substitute F for (mg.)
F|| = mg * sin θ
F|| = 100N * sin 30 degrees
F|| = 50 N
F⟂= mg * cos θ
F⟂= 100 N * cos 30 degrees
F⟂= 86.6 N
Before the Next Class Period:
Before the Next Class Period:
Practice these Math Problems Before Class!
Practice these Math Problems Before Class!
Click on the picture to take you to the practice problems that I will be going over the next time we have class. Remember, you need to try the problems on your own to see where you make your mistakes if you want to learn how to do the math problems on your own.
You have finished Lesson 4!
You have finished Lesson 4!
Be sure to head over to google classroom and fill out the exit pass.
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