## cassytaylor92 2 years ago HELP ME PLEASE ! (reposted) (Resolving Vector) A woman pushes a 50-N 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)

1. phi

Did you sketch a picture ?

2. cassytaylor92

No, I don't know how to begin it.

3. phi

|dw:1382104719667:dw|

4. phi

do you see the 25N force along the handle can be broken into sideways and up/down ? do you see you have a 45-45-90 triangle. You know the hypotenuse. can you find the length of the (equal) legs ?

5. cassytaylor92

No, i can't @phi

6. phi

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 ?

7. phi

you should get $2 x^2 = 25^2 \\ x^2 = \frac{25^2}{2} \\ x= \sqrt{\frac{25^2}{2} }= \frac{25}{\sqrt{2}}= \frac{25 \sqrt{2}}{2}$

8. cassytaylor92

25/sin 90 degrees * x/sin 45 degrees (25)(sin 45 degrees) = (x)(sin 90 degrees) i'm not really sure with this yet

9. cassytaylor92

why is it 2x^2 = 25^2 ?

10. phi

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 $x^2 + x^2 = 25^2 \\ 2x^2= 25^2$

11. phi

If the pythagoraean theorem does not ring any bells, you should learn it.

12. cassytaylor92

I got the phythagorean theorem, thanks :) Can you still help with the next step on answering it?

13. phi

now you have this picture |dw:1382106175853:dw|

14. phi

can you answer the questions? the sideways force is only the one vector the downward force is the sum of two vectors

15. cassytaylor92

Is the downward force: 25^2/2 and 50 N?

16. phi

25^2/2 means 25*25/2 do you mean $$25 \sqrt{2}/2$$ ?

17. cassytaylor92

No. What I mean is the 25 sqr(2)/2 and 50 N.

18. phi

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"

19. cassytaylor92

i'm confused with the 25 sqr(2)

20. phi

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

21. cassytaylor92

so that would be the answer for the downward force? @phi

22. phi

yes

23. cassytaylor92

thanks :) how about the force horizontally?

24. phi

look at the picture. How big is the vector that goes sideways ?

25. cassytaylor92

25 sqr(2)/2 ?

26. phi

yes. or as a decimal about 67.678 N

27. cassytaylor92

Thank you very much for helping! @phi ^_^

28. phi

yw

29. phi

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)

30. cassytaylor92

its okay. thanks for reminding :) @phi

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