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conquest said:the corner with an angle of theta is the one with an arm to the center and an arm to the F parallel axis and sine theta is equal to the opposite side divided by the hypotenuse. So indeed sin theta = F parallel / mg so F parallel = mgSin(theta) is correct.
As conquest has explained, you're imagining the wrong triangle. If you want to find the components of a vector using a right triangle, then that full vector must be the hypotenuse of that triangle. The other sides are the components. (The components are always smaller than the original vector.)Vantenkeist said:I agree, sin theta is equal to opposite divided by hypotenuse. But opposite of theta in the picture is mg, and the hypotenuse is F parallel. So that gives us Sin theta = mg/F parallel. Which makes F parallel equal to mg/sin theta...do you see the dilemma?
Doc Al said:As conquest has explained, you're imagining the wrong triangle. If you want to find the components of a vector using a right triangle, then that full vector must be the hypotenuse of that triangle. The other sides are the components. (The components are always smaller than the original vector.)
Since you want the components of the weight, then it's the weight that must be the hypotenuse of your right triangle.
You can certainly construct a triangle, as you did, where the weight (mg) is one of the sides. But the hypotenuse will not be the component of the weight parallel to the incline. (That triangle has no physical meaning and its hypotenuse is mislabeled.)Vantenkeist said:Thank you I will look into this a little more. As I understand geometry, as long as you can validly construct the triangle, it cannot be a 'wrong' triangle. Any and all triangles that I could construct validly using the information given should lead to the same result. I know there's an error here - I just have to find it.
Doc Al said:You can certainly construct a triangle, as you did, where the weight (mg) is one of the sides. But the hypotenuse will not be the component of the weight parallel to the incline. (That triangle has no physical meaning and its hypotenuse is mislabeled.)
The problem is not with the geometry of triangles, but with using a right triangle to represent a physical situation.
Another hint: The component vectors must be perpendicular to each other.
An inclined plane is a simple machine that consists of a flat surface that is tilted at an angle. It is used to make it easier to move objects from a lower point to a higher point by reducing the amount of force needed to lift the object.
An inclined plane works by increasing the distance over which a force is applied. This reduces the amount of force needed to move an object up the incline. The longer the inclined plane, the less force is required to move an object up the incline.
Inclined planes can be found in many everyday objects such as ramps, stairs, and even playground slides. They are also used in construction, for example, when building a wheelchair ramp or a road that goes up a hill.
An inclined plane allows us to move heavy objects with less force, making it easier and safer to transport them. It also allows us to move objects to higher places without having to lift them straight up, which can be difficult and dangerous.
One disadvantage of using an inclined plane is that it requires more space compared to lifting an object straight up. It also increases the distance an object needs to travel, so it may take longer to move an object using an inclined plane compared to lifting it straight up. Additionally, inclined planes can be less efficient for moving heavy objects over a long distance as they may require multiple inclines or a very long incline.