Inclined Planes - Mr. Mackenzie's Web Page
NEWTON’S LESSON 11 INCLINE PLANES
We see ramps that access many buildings; these are common and obvious examples of
inclined planes.
What are some other examples of inclined planes that you come across regularly?
A sloped road or driveway, a path up a hill, and the up or down sections of a roller
Coaster, staircase to the top of the empire state building
Are there advantages to using an inclined plane? How does an inclined plane make a job seem easier?
Force: An investigation
For this investigation we’ll need:
• A board
• A heavy block
• A rope
• A spring scale
First we:
1. Attach the spring scale to the block, then pull straight up by the rope (just enough to lift the block).
2. How much force just sets the block in motion?
Then we:
1. Place the block at the bottom of the board.
2. Attach the spring scale to the block and pull it along the incline so that it is just set into motion.
3. How much force just sets the block in motion?
What do you notice about these two forces?
It takes less force to slide the blocks along the incline than to lift them straight up. But you must exert the smaller force through a larger distance to get them to the top of the table.
1. Suppose you make the incline steeper, that is, make the angle of incline greater.
How will that change the force you must exert to move the block along the incline?
2. Now suppose you make the incline less steep, that is, lay the board flat on the floor. How will that change the force you must exert to move the block along the board?
The demonstrations show that as the angle of incline increases, the force required to move the blocks at constant speed increases, also.
A thought investigation:
So, you want to get the block to the top of the table. You know that you need to exert a smaller force to push or pull the blocks up the incline when the angle of incline is smaller.
If the force to get the object to the table top decreases with a smaller incline angle, what is the trade-off?
Distance is the trade off. The smaller the incline the longer the distance to move the object.
The distance to move the block to the table top is shortest when the angle of incline is the largest, 90o to the table.
[pic]
The mechanical advantage of an inclined plane is the ratio of the length of the sloped surface to the height it spans. When the distance is vertical, mechanical advantage is 1. The higher the mechanical advantage, the less force is needed to push or pull the object to the required height.
The ancient Egyptians figured this out over 3,000 years ago when they built their pyramids. They used long, shallow ramps to help them move the heavy stones to the top!
INCLINE PLANES AND ACCELERATION
An object placed on a incline plane will often slide down the surface.
DEMO:
Put a block on a plane and tilt it at varying degrees from horizontal to vertical. What do you notice?
As the slope of the incline plane increases, what happens to the rate at which the object will slide down it?
What happens when the incline is vertical? The acceleration on the object would be equal to the acceleration due to gravity.
Objects are known to accelerate down inclined planes because of an unbalanced force. Two forces acting upon a crate which is positioned on an inclined plane (assumed to be friction-free).
• the force of gravity and the normal force. The force of gravity (also known as weight) acts in a downward direction;
• the normal force acts in a direction perpendicular to the surface (in fact, normal means "perpendicular").
[pic]
The process of analyzing the forces acting upon objects on inclined planes will involve resolving the weight vector (Fgrav) into two perpendicular components.
- one directed parallel to the inclined surface and
- the other directed perpendicular to the inclined surface.
[pic]
The perpendicular component of the force of gravity is directed opposite the normal force and as such balances the normal force.
The parallel component of the force of gravity is not balanced by any other force.
This object will subsequently accelerate down the inclined plane due to the presence of an unbalanced force.
It is the parallel component of the force of gravity which causes this acceleration. The parallel component of the force of gravity is the net force.
[pic]
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EXAMPLE: A 5.0 kg mass is placed on an incline titled at 15º.
[pic]
1. How much does the 5-kg mass weigh?
Fg = ma = 5*9.8 = 49 N
2. Calculate the magnitude of the component that is acting parallel to the incline's surface?
[pic]
3. Calculate the magnitude of the component that is acting perpendicular to the incline's surface?
[pic]
4. At what angle would these two components be equal in magnitude?
45o
5. In which range of angles would Fx > Fy? (force down the ramp be greater than force into the surface of the ramp) (a) 0º ................
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