Vectors help!!!! (1 Viewer)

Run hard@thehsc · Nov 24, 2021

How do you solve this question? (at least the first part for question 19...)

ExtremelyBoredUser · Nov 24, 2021

Run hard@thehsc said:
View attachment 34166
View attachment 34167
How do you solve this question? (at least the first part for question 19...)

the red vectors are the sin components of mg, which is the weight force of the objects.

a.

$F = T - mg\sin(\theta)$
$ma = T - mg\sin(\theta)$
$ma + mg\sin(\theta) = T$
$3a + 3g\sin(\theta) = T_{1}$ as m = 3

b.

$F = mg\sin(2\theta) - T$ double the angle as in the diagram
$T = mg\sin(2\theta) + F$
$T = mg\sin(2\theta) + ma$
$T_{2} = 2g\sin(2\theta) + 2a$ m=2 on this section

c.

a = 0 when the system is in equilibrium and tension in the rope is the same
$T_{2} = T_{1}$
$2g\sin(2\theta) + 2a = 3a + 3g\sin(\theta)$
$2g\sin(2\theta)= 3g\sin(\theta)$
$2\sin(2\theta)= 3\sin(\theta)$ divide by g
$2\sin(2\theta) - 3\sin(\theta) = 0$
$4\sin(\theta)\times\cos(\theta) - 3\sin(\theta) = 0$ double angle formula
$\sin(\theta)\times(4\cos(\theta) - 3) = 0$

$4\cos(\theta) = 3$
$cos(\theta) = \frac{3}{4}$

as required

vishnay · Nov 24, 2021

ExtremelyBoredUser said:
View attachment 34171
the red vectors are the sin components of mg, which is the weight force of the objects.

a.

$F = T - mgsin(\theta)$
$ma = T - mgsin(\theta)$
$ma + mgsin(\theta) = T$
$3a + 3gsin(\theta) = T_{1}$ as m = 3

b.

$F = mgsin(2\theta) - T$ double the angle as in the diagram
$T = mgsin(2\theta) + F$
$T = mgsin(2\theta) + ma$
$T_{2} = 2gsin(2\theta) + 2a$ m=2 on this section

c.

a = 0 when the system is in equilibrium and tension in the rope is the same
$T_{2} = T_{1}$
$2gsin(2\theta) + 2a = 3a + 3gsin(\theta)$
$2gsin(2\theta)= 3gsin(\theta)$
$2sin(2\theta)= 3sin(\theta)$ divide by g
$2sin(2\theta) - 3sin(\theta) = 0$
$4sin(\theta)*cos(\theta) - 3sin(\theta) = 0$ double angle formula
$sin(\theta) * (4cos(\theta) - 3) = 0$

$4cos(\theta) = 3$
$cos(\theta) = \frac{3}{4}$

as required

for trig functions u can do \sin like this $\sin \text{or} \cos$

and also u dont have to do asterisk just do \times like this $\times$

ExtremelyBoredUser · Nov 24, 2021

vishnay said:
for trig functions u can do \sin like this $\sin \text{or} \cos$

and also u dont have to do asterisk just do \times like this $\times$

thx

Run hard@thehsc · Nov 24, 2021

@ExtremelyBoredUser Thanks for your help. I got the first two after trying and realised the third one after seeing your working out!

Vectors help!!!! (1 Viewer)

Run hard@thehsc

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ExtremelyBoredUser

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vishnay

God

ExtremelyBoredUser

Bored Uni Student

Run hard@thehsc

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