Applications of Dot Product: Finding Force Components on an Inclined Plane

In summary, for Question 15, the magnitude of the force tending to lift the crate vertically is 108.3 N. This can be found by using the formula Fx = F.cos theta and Fy = F.sin theta to break down the applied force into x and y components, and then using basic geometry to solve for the magnitude of the vertical force.
  • #1
Macleef
30
0

Homework Statement



15) In Question 14, if the ramp makes an angle of 20 degrees with the level ground. Find the magnitude of the force tending to lift the crate vertically.

Textbook Answer for Question 15: 108.3 N

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14) A crate is being dragged up a ramp by a 125 N force applies at an angle of 40 degrees to the ramp. Find the magnitude of the force in the direction of motion (Answer is 95.8 N).

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Homework Equations



u (dot) v = |u||v|cosx

The Attempt at a Solution



I have half of the diagram because I don't understand the rest of the problem:

2czu7hl.png
 
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  • #2
draw a box on the ramp;
in FBD= W points down and your points up in +ve y ...
and box is stationary so Fnet = 0
 
  • #3
What? I don't understand what you meant by "in FBD= W points down and your points up in +ve y"
 
  • #4
i meant your force, that is asked, and W is the weight of the box
ops, sorry I missed force ><

and then this leaves you with a simply geometric problem where you find the thetas, and something simple like Fx = F.cos theta and Fy = F.sin theta
(it isn't much of dot product problem, but just dividing the F into x and y components )

This is a very common example and you can find a related example in your book too ^_^
 

Related to Applications of Dot Product: Finding Force Components on an Inclined Plane

1. What is the dot product used for in physics?

The dot product is a mathematical operation used in physics to calculate the work done by a force on an object, as well as the angle between two vectors.

2. How is the dot product applied in computer graphics?

In computer graphics, the dot product is used to determine the angle between two vectors, which can then be used to calculate the shading and lighting effects on a 3D object.

3. Can the dot product be used in statistics or data analysis?

Yes, the dot product can be used in statistics and data analysis to determine the similarity or correlation between two sets of data.

4. How does the dot product relate to the concept of projection?

The dot product can be used to project a vector onto another vector, which is useful in determining the magnitude and direction of a component of a force or velocity in a certain direction.

5. Are there any real-life applications of the dot product?

Yes, the dot product has many real-life applications such as in navigation and GPS systems, engineering and construction, and even in finance and economics for calculating risk and return on investments.

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