Answer:
1) 17 N
2) -3 N
3) 14.80 N
4) 4.18 N
5) 12.21 N
Explanation:
The resultant (R) of two forces P and Q acting at an angle θ is given by
[tex]R=\sqrt{P^2+Q^2+2PQcos\theta }[/tex]
We have P = 7N and Q =10N
1) The forces are parallel and act in the same direction ( θ = 0° )
[tex]R=\sqrt{7^2+10^2+2*7*10*cos0}=\sqrt{(7+10)^2)}=17N[/tex]
2) The forces are parallel and act in opposite directions( θ = 180° )
[tex]R=\sqrt{7^2+10^2+2*7*10*cos180}=\sqrt{(7-10)^2)}=-3N[/tex]
3) The forces are inclined at an angle of 60° to each other( θ = 60° )
[tex]R=\sqrt{7^2+10^2+2*7*10*cos60}=14.80N[/tex]
4) The forces are inclined at an angle of 160°( θ = 160° )
[tex]R=\sqrt{7^2+10^2+2*7*10*cos160}=4.18N[/tex]
5) The forces act at 90° to each other( θ = 90° )
[tex]R=\sqrt{7^2+10^2+2*7*10*cos90}=12.21N[/tex]
