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# Basic mechanics watch

1. Hiya, I would appreciate if someone could help me with this.

A smooth wire is being bent into the shape of the graph y = x + 2sin x for 0 < x < 2pi, the units being metres. Points A, B and C on the wire have coordinates (0,0) (pi, pi) and (2pi, 2pi). A bead of mass m kg is projected along the wire from A with speed u m/s so that it has enough energy to reach B but not C. Prove that u is between 8.66 and 11.10 (to 2 decimal places) and that the speed at B is atleast 3.66 m/s.

I have shown u < 11.1 (by using the principle of the conservation of mechanical energy between points A and C) but doing the same at B (or the highest point between A and B which is (2/3 pi, 2/3 pi + root3) I belive doesn't get me the right number.

2. (Original post by ElMoro)
Hiya, I would appreciate if someone could help me with this.

A smooth wire is being bent into the shape of the graph y = x + 2sin x for 0 < x < 2pi, the units being metres. Points A, B and C on the wire have coordinates (0,0) (pi, pi) and (2pi, 2pi). A bead of mass m kg is projected along the wire from A with speed u m/s so that it has enough energy to reach B but not C. Prove that u is between 8.66 and 11.10 (to 2 decimal places) and that the speed at B is atleast 3.66 m/s.

I have shown u < 11.1 (by using the principle of the conservation of mechanical energy between points A and C) but doing the same at B (or the highest point between A and B which is (2/3 pi, 2/3 pi + root3) I belive doesn't get me the right number.

I get 8.66 using the height of maximum prior to B to find the minimum velocity required. So it's probably an arithmetic slip; if you're still not getting that, then post your working.

Edit: Oops. Wrong point.
3. (Original post by ghostwalker)
I get 8.66 using the height of B to find the minimum velocity required. So it's probably an arithmetic slip; if you're still not getting that, then post your working.
Ok, using the minimum speed at B gives me the right answer but I can't see how to get that minimum speed or how I can show u > 8.66 without it.

From there I'm stuck.

4. Sorry, mistyped. You need the KE at the point which is a maximum prior to B (where x = 2pi/3) to be greater than zero.

Otherwise it won't get past that point, and can't reach B.
5. (Original post by ghostwalker)
Sorry, mistyped. You need the KE at the point which is a maximum prior to B (where x = 2pi/3) to be greater than zero.

Otherwise it won't get past that point, and can't reach B.

Thanks!

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