## katherinekc Group Title 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 one year ago one year ago

1. youarestupid Group Title

write something down if YOU want a medal

2. katherinekc Group Title

i just need help on the problem please!

3. youarestupid Group Title

plus I am sorry but I do not know the answer

4. Tushara Group Title

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 Group Title

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 Group Title

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 Group Title

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

8. geerky42 Group Title

Just do what @Tushara told you to do.

9. katherinekc Group Title

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

10. mathstudent55 Group Title

|dw:1359302350812:dw|

11. geerky42 Group Title

|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 Group Title

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

13. mathstudent55 Group Title

|dw:1359302475063:dw|

14. katherinekc Group Title

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 Group Title

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 Group Title

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

17. katherinekc Group Title

but now where do i go ?

18. mathstudent55 Group Title

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

19. katherinekc Group Title

whhat do u mean?

20. mathstudent55 Group Title

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

21. mathstudent55 Group Title

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

22. katherinekc Group Title

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

23. mathstudent55 Group Title

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

24. katherinekc Group Title

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

25. katherinekc Group Title

okay the it would be ..

26. mathstudent55 Group Title

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 Group Title

ok i got the 70 and 170 mixed around

28. mathstudent55 Group Title

There is no 70.

29. katherinekc Group Title

i mean 60*

30. katherinekc Group Title

sorry!

31. mathstudent55 Group Title

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 Group Title

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 Group Title

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 Group Title

i need to complete the problem?

35. mathstudent55 Group Title

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

36. katherinekc Group Title

okay .. and thats all i do then right

37. katherinekc Group Title

but i have to find the direction and magnitude?

38. katherinekc Group Title

??

39. mathstudent55 Group Title

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 Group Title

how do i do that?

41. mathstudent55 Group Title

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 Group Title

yes