# Vectors Question (1 Viewer)

#### hmim

##### Member

Hey, does someone know how to do 19c? If so that would be greatly appreciated, thanks!

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#### ExtremelyBoredUser

##### Bored Uni Student

Question has been answered here, albeit quite a while ago.

P.S Feel free to post answers anyways, its better if there's multiple ways posted since OP can have more methods.

#### wizzkids

##### Active Member
This question 19 Part (c) is not so hard.
Step 1. Recognise that for each mass on the string, the tension force is the same. Also recognise that the forces on the system are both masses experience the force of gravity vertically downwards.
Step 2. Decompose the force of gravity on each mass into orthogonal vectors, one vector that is normal to the inclinded plane, and another vector that is parallel to the inclined plane.
Step 3. At equilibrium, the two vectors that are parallel to their respective inclined planes will be equal. If the system is not at equilibrium, then they will not be equal, and there will be a net force on the system making it move.
At equilibrium, m1g sin θ = m2g sin 2θ where m1 = 3 and m2 = 2
next you are going to need the following trigonometric identity:
sin 2θ = 2 sinθ cosθ

Do you think you can do the rest of the calculation now?

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#### hmim

##### Member
This question 19 Part (c) is not so hard.
Step 1. Recognise that for each mass on the string, the tension force is the same. Also recognise that the forces on the system are both masses experience the force of gravity vertically downwards.
Step 2. Decompose the force of gravity on each mass into orthogonal vectors, one vector that is normal to the inclinded plane, and another vector that is parallel to the inclined plane.
Step 3. Equate the two vectors that are parallel to their respective inclined planes.
i.e. m1g sin θ = m2g sin 2θ
next you are going to need the following trigonometric identity:
sin 2θ = 2 sinθ cosθ

Do you think you can do the rest of the calculation now?
Hmmm... I was wondering how they would use part a and b for it. Do you mind showing your working out for it?

#### wizzkids

##### Active Member
Yes, I could show you the working, but I'm not going to do that.
As a teacher, I believe you should use the hints I have given you to work it out for yourself.
Sorry!

#### ExtremelyBoredUser

##### Bored Uni Student
Hmmm... I was wondering how they would use part a and b for it. Do you mind showing your working out for it?
Yea I agree with sir above, just struggle for a bit and if you can't get it at all, just check the thread i posted above for sols.

Trust, its worth it spending an hr or something like that on a hard problem (using hints is fine) bc when u get it you'll already self-teach how to solve a hard problem, what techniques to use and how to + you'll understand the concept by virtue of proving it yourself.

But I wouldn't waste a week on it and then burn out, if you really can't get it, just move on or just check the sols and attempt a similar vectors Q.

#### hmim

##### Member
Yea I agree with sir above, just struggle for a bit and if you can't get it at all, just check the thread i posted above for sols.

Trust, its worth it spending an hr or something like that on a hard problem (using hints is fine) bc when u get it you'll already self-teach how to solve a hard problem, what techniques to use and how to + you'll understand the concept by virtue of proving it yourself.

But I wouldn't waste a week on it and then burn out, if you really can't get it, just move on or just check the sols and attempt a similar vectors Q.
thanks!