mechanics

[Light]

1)each of 2 forces has magnitude X N and the resultant of 2 forces has magnitude 12N.when magnitude of 1 force increases by 70%,the magnitude of 2 forces becomes 21N.find X and angle between 2 forces.

2)a force F of magnitude 12N has components P and Q.The sum of magnitude of P and Q is 18N.the direction of Q is at right angle to F.Find magnitude of Q.

[Light]

Anyone?pls help.

[astarmathsandphysics]

I will when I get up

[astarmathsandphysics]

1)each of 2 forces has magnitude X N and the resultant of 2 forces has magnitude 12N.when magnitude of 1 force increases by 70%,the magnitude of 2 forces becomes 21N.find X and angle between 2 forces.
Resolve in the direct of one of the forces. If y is the ang;e bewtten them.
x+xcosy y=12               (1)
1.7x+xcosy=21              (2)
(2)-(1)
0.7x=9 so x=9/0.7=90/7
cosy=(12-x)/x from (1)
cosy=(12-90/7)/(90/7)=-1/15 sp y=arccos(-1/15)=93.8degrees

[astarmathsandphysics]

a force F of magnitude 12N has components P and Q.The sum of magnitude of P and Q is 18N.the direction of Q is at right angle to F.Find magnitude of Q.
|P|+|Q|=18                        (1)
sqrt(|P|^2+|Q|^2)=12         (2)
from (1) |P|^2+2|P||Q|+|Q|^2 =324
from (2) (|P|^2+|Q|^2=144 

the difference between these 2 is 2|P||Q|=190 so |P||Q|=90 so |P|=90/|Q| sub into (1)
90/|Q|+|Q|=18
90+|Q|^2=18|Q|
|Q|^2-18|Q|+90=0
This equation has no solutions. Can you check the question?

[Light]

erm,both answers wrong .but i managed to find the answers at last .thx.

[Saladin]

It is an unlikely event that astar is wrong.

[astarmathsandphysics]

I checked my answers. Cant find anything wrong.