## katherinekc 2 years ago Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer. show work

1. youarestupid

write something down if YOU want a medal

2. katherinekc

i just need help on the problem please!

3. youarestupid

plus I am sorry but I do not know the answer

4. Tushara

calculate the vertical and horizontal components of each force, and then all the vertical forces together, then add horizontal forces together... after that u can combine the vertical and horizontal vector using pythagaros theorem to get the resulting force

5. katherinekc

im not sure how to do all that .. im horrible in math and im just trying to pass so i can be done:(

6. katherinekc

I know i have to resolve each vector into horizontal and vertical components using sin and cos but im not sure how to actually begin

7. geerky42

Always try to sketch. It may help you.|dw:1359302063400:dw|

8. geerky42

Just do what @Tushara told you to do.

9. katherinekc

i just dont know where or how to really do it :/

10. mathstudent55

|dw:1359302350812:dw|

11. geerky42

|dw:1359302341604:dw|$\Large \sin \theta = \dfrac{y}{r} \Rightarrow r \sin \theta = y$$\Large \cos \theta = \dfrac{x}{r} \Rightarrow r \cos \theta = x$

12. katherinekc

but how would i put this all into writing to show my work? like in step form?

13. mathstudent55

|dw:1359302475063:dw|

14. katherinekc

i began with this.. is this a good start; f1x= 200cos(60) f1x= 100 cos (170) rx= 200 cos(60) + 100 cos(170)

15. mathstudent55

F1 = 200, F2 = 100 F1x = F1 cos 60 F1y = F1 sin 60 F2x = f2 cos 170 F2x =F2 sin 170 Rx = F1x + F2x Ry = F1y + F2y R(theta) = tan^1(Ry/Rx)

16. mathstudent55

On the second line, you mean f2x, but that's good.

17. katherinekc

but now where do i go ?

18. mathstudent55

Now do the same for the force components in the y direction.

19. katherinekc

whhat do u mean?

20. mathstudent55

Do this: f1x= 200cos(60) f2x= 100 cos (170) rx= 200 cos(60) + 100 cos(170) For F1y, F2y, and Ry

21. mathstudent55

F1y = F1 sin 170 F2y = ... Ry = F1y + F2y = ...

22. katherinekc

f1y = 100 sin (170) f2y = 200 sin ( ) ?? hmm

23. mathstudent55

F1 = 200, F2 = 100. You switched them.

24. katherinekc

f1 = 200 sin (170) f2 = 100 sin (60) ??

25. katherinekc

okay the it would be ..

26. mathstudent55

You got the x-components above and you did it correctly. Now you need the y-components. f1y = 200 sin (60) f2y = 100 sin (170) Ry = f1y + f2y = 200 sin 60 + 100 sin 170

27. katherinekc

ok i got the 70 and 170 mixed around

28. mathstudent55

There is no 70.

29. katherinekc

i mean 60*

30. katherinekc

sorry!

31. mathstudent55

Remember the first force, F1, is 200 lb at 60 deg The x component is F1x = 200 cos 60 The y component is F1y = 200 sin 60 The second force, F2, is 100 lb at 170 deg The x component is F2x = 100 cos 170 The y component is F2y = 100 sin 170 The resultant's x-component is Rx = F1x + F2x = 200 cos 60 + 100 cos 170 The resultant's y-component is Ry = F1y + F2y = 200 sin 60 + 100 sin 170

32. mathstudent55

Now you need to do the actual calculations with a calculator of what Rx and Ry are, and round off to 2 decimal places.

33. katherinekc

so all i have to do is put the equation in the calculator for rx and ry and thatll give me the answers?

34. katherinekc

i need to complete the problem?

35. mathstudent55

For now, yes. That will give you the x- and y-components of the resultant.

36. katherinekc

okay .. and thats all i do then right

37. katherinekc

but i have to find the direction and magnitude?

38. katherinekc

??

39. mathstudent55

Once you have the x- and y-components of the resultant, you need two more steps. 1. You need to find the magnitude of the resultant. 2. You need to find the direction of the resultant.

40. katherinekc

how do i do that?

41. mathstudent55

For the magnitude of the resultant, you use the Pythagoras theorem. For the direction of the resultant, you use the inverse tangent to get the angle. See figure below: |dw:1359304507660:dw|

42. mathstudent55

yes

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