Vector forces on ring

p75213 · #1 $Old$ November 1st, 2009, 05:07 PM

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?

Grandad · #2 $Old$ November 2nd, 2009, 03:36 AM

Hello p75213

Welcome to Math Help Forum!

Quote:

Originally Posted by p75213 $View Post$

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 $F$ acts outwards from the origin $O$ along a line that makes a direction $\theta$ measured anticlockwise from the positive direction of $Ox$ , then its components along $Ox$ and $Oy$ are

$F\cos\theta$ and $F\sin\theta$ , respectively

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

Along $ON$ :

$N: -58$

$M: 105\cos73^o = 30.70$

$L: -40\cos149^o=34.29$

$K: 72\cos194^o =-69.86$

Perpendicular to $ON$ :

$N: 0$

$M: 105\sin73^o=100.41$

$L: -40\sin149^o=-20.60$

$K: 72\sin194^o=-17.42$

We find the resultant force by summing these components:

Along ON: $-62.87$

Perpendicular to ON: $62.4$

The magnitude of the resultant is therefore $\sqrt{62.87^2+62.4^2}=88.58$ .

Grandad

p75213 · #3 $Old$ November 2nd, 2009, 03:55 AM

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