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vertical circular motion and forces (M2)

Hi guys ,
I'm practising a vertical circular motion question where a particle of certain mass m kg and length L(which is equal to the radius of the circle) is moving about O with different angles . The increase in length each time the particle moves from one point to another through different angles has been successfully calculated and written below the points on the attachment for points 1,2 and 3 but for point 4 I'm a bit unsure about my answer which is 2L+Lcos40 . Can anyone correct me if I'm wrong here please . thanks

12903849_2007190056171988_1151602351_o.jpg181.2KB

Reply 1

B_9710

Height ,

\displaystyle h=l+l\cos \theta

(edited 8 years ago)

Reply 2

Alen.m

Original post by B_9710

Height ,

\displaystyle h=l-l\cos \theta

That's what i did for point 1 . My problem is height on point 4

Reply 3

B_9710

Original post by Alen.m

That's what i did for point 1 . My problem is height on point 4

The same formula for the height should still work.
So the height will be

l(1-\cos (220^{\circ} ))

.
How did you get 2l in your expression for h at point 4?
It might be worth noting that if

h=l(1-\cos 220^{\circ} ) \text{ then h} =l(1+\cos 40^{\circ} )

(edited 8 years ago)

Reply 4

Alen.m

Original post by B_9710

The same formula for the height should still work.

So you reckon the answer would be L-Lcos220?

Reply 5

Alen.m

Original post by B_9710

The same formula for the height should still work.
So the height will be

l(1-\cos (220^{\circ} )

But you see on point 2 the answer is completely different

Reply 6

Alen.m

Original post by B_9710

The same formula for the height should still work.
So the height will be

l(1-\cos (220^{\circ} )

.
How did you get 2l in your expression for h at point 4?

2L is the height on point three

Reply 7

B_9710

Original post by Alen.m

2L is the height on point three

I see what you've done. Remember that height is measured from point 3, so the height at point 3 is 0. What you've done is find the distance from the top of the circle, which is not the height.

(edited 8 years ago)

Reply 8

Alen.m

Original post by B_9710

I see what you've done. Remember that height is measured from point 3, so the height at point 3 is 0. What you've done is find the distance from the top of the circle, which is not the height.

Well actually the reason i said height is because i need that to use in mgh formula to get G.P.E. The question requires me to find G.P.E and use that in the principle of conservation of mechanical energy to find velocity at different points so i assumed i need to know the height of particle at different points as it moves around the circle

Reply 9

Alen.m

Perhaps you're right i need to find the distance from the top of the circle and use that as h in formula for G.P.E is that right?

Reply 10

B_9710

Original post by Alen.m

Perhaps you're right i need to find the distance from the top of the circle and use that as h in formula for G.P.E is that right?

No you need to find the height which is the distance to the bottom of the circle to the object. We are taking the the base level to be the height at the bottom of the circle.

Reply 11

Alen.m

Original post by B_9710

No you need to find the height which is the distance to the bottom of the circle to the object. We are taking the the base level to be the height at the bottom of the circle.

Oh right i think the confussion made by me coz im taking the point where the particle arrives at each time through different angle as a base level

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