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cassytaylor92
 2 years ago
HELP ME PLEASE ! (reposted)
(Resolving Vector) A woman pushes a 50N lawn mower with a force of 25 N. If the handle of the lawn mower is 45 degrees above the horizontal, how much downward force is the lawn mower exerting on the ground? How much force causes the motion of the lawn mower horizontally?(neglect friction)
cassytaylor92
 2 years ago
HELP ME PLEASE ! (reposted) (Resolving Vector) A woman pushes a 50N lawn mower with a force of 25 N. If the handle of the lawn mower is 45 degrees above the horizontal, how much downward force is the lawn mower exerting on the ground? How much force causes the motion of the lawn mower horizontally?(neglect friction)

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cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0No, I don't know how to begin it.

phi
 2 years ago
Best ResponseYou've already chosen the best response.2do you see the 25N force along the handle can be broken into sideways and up/down ? do you see you have a 454590 triangle. You know the hypotenuse. can you find the length of the (equal) legs ?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2to do this problem you need to know some physics and some math Let's start with the math dw:1382105210794:dw can you solve for x ?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2you should get \[ 2 x^2 = 25^2 \\ x^2 = \frac{25^2}{2} \\ x= \sqrt{\frac{25^2}{2} }= \frac{25}{\sqrt{2}}= \frac{25 \sqrt{2}}{2} \]

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.025/sin 90 degrees * x/sin 45 degrees (25)(sin 45 degrees) = (x)(sin 90 degrees) i'm not really sure with this yet

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0why is it 2x^2 = 25^2 ?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2First, using the Law of Sines works. sin 45 = sqr(2)/2 and sin 90 = 1 you get x= 25 sqr(2)/2 which is good. I used geometry. you have a right triangle which is also isosceles, so its 2 sides are equal. You can use pythagorean theorem a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse \[ x^2 + x^2 = 25^2 \\ 2x^2= 25^2\]

phi
 2 years ago
Best ResponseYou've already chosen the best response.2If the pythagoraean theorem does not ring any bells, you should learn it.

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0I got the phythagorean theorem, thanks :) Can you still help with the next step on answering it?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2now you have this picture dw:1382106175853:dw

phi
 2 years ago
Best ResponseYou've already chosen the best response.2can you answer the questions? the sideways force is only the one vector the downward force is the sum of two vectors

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0Is the downward force: 25^2/2 and 50 N?

phi
 2 years ago
Best ResponseYou've already chosen the best response.225^2/2 means 25*25/2 do you mean \( 25 \sqrt{2}/2\) ?

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0No. What I mean is the 25 sqr(2)/2 and 50 N.

phi
 2 years ago
Best ResponseYou've already chosen the best response.2then yes, you add those two values... the vectors are pointing in the same direction so you can just add their lengths to get the total length of the "resultant vector"

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0i'm confused with the 25 sqr(2)

phi
 2 years ago
Best ResponseYou've already chosen the best response.2first, it is \[ \frac{25\sqrt{2}}{2} \] you can add 50 to it like this: \[ 50+ \frac{25\sqrt{2}}{2} \] that is an exact answer. you can use a calculator and find a decimal number, but you will have to round the decimal number (because in theory the answer has an infinite number of digits on the right side of the decimal point) see http://www.wolframalpha.com/input/?i=+100+digits+of+50+%2B+25*sqrt%282%29%2F2

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0so that would be the answer for the downward force? @phi

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0thanks :) how about the force horizontally?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2look at the picture. How big is the vector that goes sideways ?

phi
 2 years ago
Best ResponseYou've already chosen the best response.2yes. or as a decimal about 67.678 N

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you very much for helping! @phi ^_^

phi
 2 years ago
Best ResponseYou've already chosen the best response.2oops I just noticed I posted the wrong decimal value for the horizontal force 25* sqrt(2)/2 is about 17.678 N (NOT 67.678 N which is the downward force)

cassytaylor92
 2 years ago
Best ResponseYou've already chosen the best response.0its okay. thanks for reminding :) @phi
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