How Do You Calculate the Magnitude of a Resultant Vector from Multiple Forces?

[nettie2311]

Homework Statement

Find the magnitude of the resultant of the following series of vectors.

120N, North
190N, 60 degrees East of North
70N, 10 degrees East of South
150N, 45 degrees South of West

I have similar questions like these and not sure how to answer them, if anyone can help it would be greatly appreciated.

 

[rock.freak667]

Start by drawing a diagram with all the forces, draw the 4 directions and then sketch the forces.

Try resolving each of the forces.

 

[nettie2311]

Thanks for the reply, but physics is totally new to me and I've been online to try to teach myself but I'm having no luck...can you be more specific.

 

[rock.freak667]

See here for more information about resolving forces.

 

[rwisz]

I would approach this problem by first converting all the given vectors into Cartesian coordinates. This will allow us to add them together and find the resultant vector.

To convert the given vectors into Cartesian coordinates, we can use the following equations:

- For the North and South components: N = cos(theta) * magnitude and S = -cos(theta) * magnitude
- For the East and West components: E = sin(theta) * magnitude and W = -sin(theta) * magnitude

Using these equations, we can calculate the Cartesian coordinates for each of the given vectors:

- 120N, North: (0, 120)
- 190N, 60 degrees East of North: (95*sqrt(3), 95)
- 70N, 10 degrees East of South: (7*tan(10), -70)
- 150N, 45 degrees South of West: (-150*sqrt(2)/2, -150*sqrt(2)/2)

Now, we can add these coordinates together to find the resultant vector:

R = (0 + 95*sqrt(3) - 150*sqrt(2)/2, 120 + 95 - 70 - 150*sqrt(2)/2)
= (95*sqrt(3) - 150*sqrt(2)/2, 95 - 150*sqrt(2)/2)

To find the magnitude of this resultant vector, we can use the Pythagorean theorem:

|R| = sqrt((95*sqrt(3) - 150*sqrt(2)/2)^2 + (95 - 150*sqrt(2)/2)^2)
= 166.3 N

Therefore, the magnitude of the resultant is 166.3 N. I would also suggest double-checking the calculations and using appropriate units for the final answer.