Question

Two force vectors,
F1 = (-3.0 N) x-hat + (-2.5 N) y-hat
and
F2 = (-6.0 N) x-hat + (3.5 N) y-hat
are applied to a particle. What third force F3 would make the net force on the particle zero?

Answer 1

Are you familiar with the bra -ket vector notation
F1 = <a,b> = < -3 , -2.5>
?

Answer 2

Nope. :0

Answer 3

ok, it is just that, the x and y components

Answer 4

This is technically for a physics class but no one in the physics section on here is helping me

Answer 5

You want to find a third force F3, so that the object does not accelerate,

Answer 6

Net force is Zero

\[F _{NET} = F _{1}+F _{2}+F _{3}\]

Answer 7

With vector addition, you can simply add the components of each dimension together...

Answer 8

Instead of using the unit vector multiplier x-hat and y hat, it is simpler with <a,b> where a is multiplied by x-hat and b is by y-hat

Answer 9

\[<0 , 0> = <-3.0 ,~ -2.5> + <-6.0,~ 3.5> + <a,b>\]

Answer 10

\[F _{3}= a* xroof + b*yroof = \]

Answer 11

So would it be <9,-1>?

Answer 12

F3 = <a,b>

Answer 13

With that vector equation, you can solve for the a and b components of F3 by equating the x direction and the y direction values...

0 = -3.0 +(-6.0) + a [N]

Answer 14

Total force in the x direction is 0 or -3 - 6 + a, newtons,

same for Y, then you have your F3 force

Answer 15

The sum of the components in the X-direction is zero
The sum of the components in the Y-direction is zero

(all the xroofs have to equal zero)
(all the yroofs) have to equal zero)

solve for the components of the third force

Answer 16

So is that a yes or a no to being <9,-1> For F3?

Answer 17

That looks good

Answer 18

Did you do a section on vectors before this? if i remember i think there was in physics 1, maybe not