Question

Three forces act upon an object, which remains at rest. The forces are represented by the vectors P, Q and R, where

P = 5i +4j and Q = -3i +6j

Calculate the magnitude and direction in degree of vector R.

I have done this and got magnitude 10.2 and direction 78.7 degree's

Could someone please verify this or let me know where I have gone wrong. Thanks.

Answer 1

Add PandQ, R and PQ must be of same magnitude and opposite angles

Answer 2

Sorry Adrian I don't follow what you are saying. I have added P and Q to get R and made the magnitute 10.2.

Answer 3

When you add up three forces, you net forces should be zero
P = 5i +4j and Q = -3i +6j
P={5,4}
Q={-3,6}
R={-2,-10}

Answer 4

find mag and direction of R vector

Answer 5

http://www.scribblar.com/kxnfusdm3

Answer 6

\[\sqrt{4+100}=\sqrt{104}\]
=\[2\sqrt{26}\]

Answer 7

I am happy with the magnitude of 10.2 but I am being told that the direction is wrong. can you verify this??

Answer 8

2 sqrt[26] evaluate to be 10.2

\[arctan(10/2)\]=78.69
but that's wrong , remember unit circle
180-78.69=101.31

Answer 9

I dont have an option for 101.31 I have options 78.7, -11.3, -101.3, 11.3, -78.7, -168.7.

Surely the resultantvector will be between P and Q? So I don't understand where the need to take 180 - 78.7

Answer 10

Oh, I saw thinking {-2,10} instead of {-2,-10}


arctan(10/2)=78.7

but let's visualize it right this time

let's visualize

Answer 11

so 180 -78.7 =101.3
but we are doing negative angel
so -101.3

Answer 12

Ok, cool so the R vector is pulling in the opposit direction 'balancing' the forces of P and Q? Got it ... thanks a lot. Medal on its way.

Answer 13

180+78.7 is also a right answer if you go other way

Answer 14

Also remember :
net force of zero doesn't mean a object is at rest
but when item is at rest , net force is zero

Answer 15

Yeah ... sorted. Thanks. I was ignoring that the R was pulling in opposing direction. Some reason my head was saying it was a resultant of P and Q. Not quite the same! :)