mechanics question, resultant forces.

Two forces P and Q act on a particle. The force P has magnitude 7N and acts due north. The resultant of P and Q is a force of magnitude 10N acting in a direction with bearing 120 degrees. Find

i) the magnitude of Q
ii) the direction of Q, giving your answer as a bearing.

any help would be much appreciated, thanks :)

Quote:

---

Originally Posted by Oranges&Lemons

Two forces P and Q act on a particle. The force P has magnitude 7N and acts due north. The resultant of P and Q is a force of magnitude 10N acting in a direction with bearing 120 degrees. Find

i) the magnitude of Q
ii) the direction of Q, giving your answer as a bearing.

any help would be much appreciated, thanks :)

---

Use some trig...




Solve for the system of equations. Basically, you want to split all the forces into x's (top equation) and y's (bottom equation). Use the sine of an angle multiplied by the force to get the vertical force; use cosine for horizontal directions.

Quote:

---

Originally Posted by Oranges&Lemons

Two forces P and Q act on a particle. The force P has magnitude 7N and acts due north. The resultant of P and Q is a force of magnitude 10N acting in a direction with bearing 120 degrees. Find

i) the magnitude of Q
ii) the direction of Q, giving your answer as a bearing.

any help would be much appreciated, thanks :)

---

Here is another attempt:

1. draw a rough sketch

2. You can calculate the dotted green line by Cosine rule. The length of this line correspond with the magnitude of Q:



3. To calculate the bearing of Q you have to add the angle to the 120° = bearing of the resultant force R:



This will give you

And therefore the bearing of Q is 144.182°

thankyou so much!