Calculating Vector Components with given Magnitude and Direction

[rashad764]

Homework Statement

F =(70N, 57.1∘counterclockwise from positive y−axis)[/B]
Find the vector components of F

Homework Equations

Sin and Cos of the angle[/B]

The Attempt at a Solution

x is component is 38 and y component is 58
how does the angle being counterclockwise affect my answer?
The answer above is wrong

Does the length of become F negative as well as the angle?

 

[fresh_42]

Have you drawn an image? Or more straight forward: how big is the angle measured form the positive x-axis as it is usually done? Do you know the formula for the components, given the angle and the length?

 

[Mark44]

Does the length of become F negative as well as the angle?

The length of a vector is always nonnegative, but in this case, at least one of the components will be negative. As already suggested, draw a sketch of the vector.

 

[rashad764]

Have you drawn an image? Or more straight forward: how big is the angle measured form the positive x-axis as it is usually done? Do you know the formula for the components, given the angle and the length?

Don't you take the sin and cos of the angle, 70=x/cos57.1 then multiply 70(cos 57.1)

 

[fresh_42]

Don't you take the sin and cos of the angle, 70=x/cos57.1 then multiply 70(cos 57.1)

Yes, but your angle is wrong. The angle for these formulas is measured from the x-axis, but you have a number measured from the y-axis.

 

[rashad764]

Yes, but your angle is wrong. The angle for these formulas is measured from the x-axis, but you have a number measured from the y-axis.

How would I measure it from the x axis

 

[fresh_42]

Sketch it, then you will see. How big is the difference between the two measurements? Of course you could as well calculate with the given angle, but then you will have to adjust the formulas to the new situation. This leaves us with the question: How is $x= 70N \cdot \cos(57.1°)$ found?

 

[rashad764]

Sketch it, then you will see. How big is the difference between the two measurements? Of course you could as well calculate with the given angle, but then you will have to adjust the formulas to the new situation. This leaves us with the question: How is $x= 70N \cdot \cos(57.1°)$ found?

Do I draw the vector 57.1 degrees from x-axis then measure the difference

 

[HRubss]

57.1∘counterclockwise from positive y−axis

If it were from the x-axis, then the angle would be 57.1°

 

[fresh_42]

You draw the vector at 57.1 degrees from the y-axis (counterclockwise, as given) and next measure the angle from the x-axis and put this new angle into the formulas. Or you draw a triangle with the given data and calculate the side lengths of this triangle plus adjust the signs according to the drawing.

 

[rashad764]

You draw the vector at 57.1 degrees from the y-axis (counterclockwise, as given) and next measure the angle from the x-axis and put this new angle into the formulas. Or you draw a triangle with the given data and calculate the side lengths of this triangle plus adjust the signs according to the drawing.

the angle from the x-axis is 147.1

 

[fresh_42]

the angle from the x-axis is 147.1

Right. And this is the angle your formulas are made for. Otherwise you would have had to use the triangle in the second quadrant (with different formulas) and use a positive y value and a negative x value.