Applications of Dot Product

[K_Swiss]

A box with a weight of 215 N rests on a ramp. There is a frictional force of 27 N exerted on the box directed up the ramp. If the ramp is inclined at 30 degrees, what force must be applied at an angle of 40 degrees to the ramp to maintain equilibrium?

Textbook Answer: 80.5 N and 105 N

I don't even know how to draw the problem. . .I don't know how to solve this problem. . .All I know is you use the formula: "u (dot) v = |u||v|cosx"

Please walk me through this problem!

 

[MarkSA]

Sounds like me.. we just started doing this in physics. This is more a physics problem than a calculus problem I think...

I can try to explain the dot product... maybe give you some tips but I don't think I could solve this problem yet.

The dot product is the magnitude of the force times the magnitude of the displacement, multiplied by the cosine of the angle between the two vectors. magnitudes are always positive which is why the vectors have absolute value bars around them. In this case there doesn't seem to be any displacement so i'm not sure what you can do with the dot product. And I believe that the amount of Work done is equal to the dot product.

 

[tkhunny]

I hope you know more than that. Have you forgotten ALL your trig?

215*sin(30º) = 27 + X*cos(40º)

You can at least solve it this way. Now ponder the dot product.