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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)
 6 months ago
 6 months 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)
 6 months ago
 6 months ago

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phiBest ResponseYou've already chosen the best response.2
Did you sketch a picture ?
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
No, I don't know how to begin it.
 6 months ago

phiBest ResponseYou've already chosen the best response.2
do 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 ?
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
No, i can't @phi
 6 months ago

phiBest ResponseYou've already chosen the best response.2
to 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 ?
 6 months ago

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

cassytaylor92Best ResponseYou've already chosen the best response.0
25/sin 90 degrees * x/sin 45 degrees (25)(sin 45 degrees) = (x)(sin 90 degrees) i'm not really sure with this yet
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
why is it 2x^2 = 25^2 ?
 6 months ago

phiBest ResponseYou've already chosen the best response.2
First, 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 \[ x^2 + x^2 = 25^2 \\ 2x^2= 25^2\]
 6 months ago

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

cassytaylor92Best ResponseYou've already chosen the best response.0
I got the phythagorean theorem, thanks :) Can you still help with the next step on answering it?
 6 months ago

phiBest ResponseYou've already chosen the best response.2
now you have this picture dw:1382106175853:dw
 6 months ago

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

cassytaylor92Best ResponseYou've already chosen the best response.0
Is the downward force: 25^2/2 and 50 N?
 6 months ago

phiBest ResponseYou've already chosen the best response.2
25^2/2 means 25*25/2 do you mean \( 25 \sqrt{2}/2\) ?
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
No. What I mean is the 25 sqr(2)/2 and 50 N.
 6 months ago

phiBest ResponseYou've already chosen the best response.2
then 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"
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
i'm confused with the 25 sqr(2)
 6 months ago

phiBest ResponseYou've already chosen the best response.2
first, 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
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
so that would be the answer for the downward force? @phi
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
thanks :) how about the force horizontally?
 6 months ago

phiBest ResponseYou've already chosen the best response.2
look at the picture. How big is the vector that goes sideways ?
 6 months ago

phiBest ResponseYou've already chosen the best response.2
yes. or as a decimal about 67.678 N
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
Thank you very much for helping! @phi ^_^
 6 months ago

phiBest ResponseYou've already chosen the best response.2
oops 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)
 6 months ago

cassytaylor92Best ResponseYou've already chosen the best response.0
its okay. thanks for reminding :) @phi
 6 months ago
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