Thread: Vector forces on ring

The question is:- Four given pulls and thrusts act on a ring. Find their equilibrant. The pulls and thrusts are as follows:
N = 58 - thrust
M = 105 - pull
L = 40 - thrust
K = 72 - pull
Angles are as follows:
NM - 73 deg
NL - 149 deg
NK - 194 deg

The methodology I have used is calculate the equilibrium for the pulls and thrusts separately. Then subtract the thrusts from the pulls. The answer I get is 60.36, however the answer given is 88.5. Where have I gone wrong?

Hello p75213

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Originally Posted by p75213

The question is:- Four given pulls and thrusts act on a ring. Find their equilibrant. The pulls and thrusts are as follows:
N = 58 - thrust
M = 105 - pull
L = 40 - thrust
K = 72 - pull
Angles are as follows:
NM - 73 deg
NL - 149 deg
NK - 194 deg

The methodology I have used is calculate the equilibrium for the pulls and thrusts separately. Then subtract the thrusts from the pulls. The answer I get is 60.36, however the answer given is 88.5. Where have I gone wrong?

If a force acts outwards from the origin along a line that makes a direction measured anticlockwise from the positive direction of , then its components along and are

and , respectively

Since the angles are measured from the direction of , I assume they are all in the same sense (e.g. all anticlockwise). So we can write down the components along and perpendicular to , where is the ring, as follows:

Along :

Perpendicular to :

We find the resultant force by summing these components:

Along ON:

Perpendicular to ON:

The magnitude of the resultant is therefore .

Grandad

Thanks Grandad. Simple when somebody shows you where you were going wrong ie. Thrusts are negative and pulls are positive.