A level physics

A particle is in equilibrium under 4 horizontal forces:
- 5N,
-8N acting at 30 degrees,
-PN
-QN
Show that P = 9.

The answer says P is 8cos60 + 5. I get that 8cos60 gives you the vertical component of the 8N force, but I don’t get why we add that to 5 to get p total.

(edited 3 months ago)

Reply 1

nerak99

Can you have a look at how the wording of that question came out ? Maybe edit it so we have a complete question

Reply 2

Nat4695

Sorry, I edited it, hopefully that’s clearer

Reply 3

Mirwen

These forces cannot all be acting in the same direction as the object is in equilibrium. Which forces are acting in which direction?

For example, there must be a different vertical force to counteract the vertical component of the 8N at 30 degrees to the horizontal (which is 8sin30 or 8cos60 as you mentioned). However, your question states that all of the forces are horizontal.

(edited 3 months ago)

Reply 4

Nat4695

The question states they are all horizontal but that’s also partially what confused me, in the diagram 5 is upwards vertical and P downwards vertical while 8N at 30degrees acts to the left and Q acts to the right

Reply 5

Mirwen

Alright, from the diagram it can be solved. Since it is in equilibrium, the sum of the horizontal forces = 0 and the sum of the vertical forces = 0.

5-P+8sin30=0
8cos30-Q=0

From this P = 8sin30 + 5 and Q = 8cos30.

This value for P agrees with the answer.

Reply 6

Nat4695

Thank you!! But one thing, I get this however how is p the sum of vertical component and 5? If the particle is in equilibrium how can it be 9 which is would mean the downwards vertical is greater than the upwards

Reply 7

Mirwen

Basically since the 8N is acting at an angle it is pulling the object upwards slightly, by 4N (8sin30) in fact. So P has to match both this 4N AND the 5N. Therefore it's 9N.