Angle of Incline: A Basic Physics Question

In summary, the angle between the force of gravity and an inclined plane is always equal to the angle of the incline. This can be explained by using the fact that the sum of angles in a triangle is 180 degrees and noting the 60 degree angle in each triangle. If the angle of the incline were to decrease towards zero, the angle between the force of gravity and the incline would also approach zero.
  • #1
KayleighK
8
0
I have kind of a stupid question to ask, but its just something I really don't understand. So in pictures (like the one below) where an object is sitting on an inclined plane, why is it that the angle between the force of gravity and the incline plane is the same as the angle of the incline?


http://www.glenbrook.k12.il.us/gbssci/Phys/Class/vectors/u3l3e9.gif [Broken]

I don't really have a strong math background so these little things confuse me. Thanks in advance for any help.
 
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  • #2
Take a look at this diagram, featuring a 30 degree angle.
http://en.wikiversity.org/wiki/Motion_in_two_dimensions#Inclined_Planes
To understand why the other angle is 30, you must use the fact that the sum of the angles in a triangle is 180 degrees and note the 60 degree angle in each triangle (in fact the 60 degree angle is common to the two triangles).
 
  • #3
Try to visualize what would happen if the angle were to begin to approach zero, that is if the incline were to decrease towards zero. What angles in the force diagram would approach zero and which would approach a right angle?
 

1. What is the angle of incline?

The angle of incline is the angle at which an object or surface is tilted or slanted.

2. How is the angle of incline calculated?

The angle of incline can be calculated using trigonometry, specifically the inverse tangent function. The formula is tan θ = opposite/adjacent, where θ is the angle of incline, opposite is the height of the object or surface, and adjacent is the horizontal distance.

3. What is the relationship between the angle of incline and the force of gravity?

The angle of incline affects the force of gravity acting on an object. The greater the angle of incline, the less force of gravity is acting on the object. This is because the force of gravity is divided into two components: the normal force perpendicular to the surface, and the parallel force parallel to the surface. As the angle of incline increases, the normal force decreases, resulting in a smaller force of gravity acting on the object.

4. How does the angle of incline affect the motion of an object?

The angle of incline affects the acceleration of an object as it moves along the surface. The steeper the incline, the greater the acceleration will be. This is because the component of force parallel to the surface increases as the angle of incline increases, resulting in a greater net force and therefore a greater acceleration.

5. How is the angle of incline used in real-life applications?

The angle of incline is used in many real-life applications, such as designing ramps, roads, and roller coasters. It is also used in sports such as skiing and snowboarding, where the angle of the slope affects the speed and difficulty of the course. In construction, the angle of incline is also considered when building structures to ensure stability and safety.

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