September 3rd, 2015, 12:09 PM  #1 
Newbie Joined: Jun 2015 From: South Africa Posts: 27 Thanks: 0  M1  Potential energy
Points A, B and C on the wire have coordinates (0, 0), (3, 3), and (6, 6). A mkg bead is projected along the wire from A with speed u ms$^{1}$ so that it has enough energy to reach B but not C. Prove that 8.16 < u < 10.95 and that the speed at B $\geqslant$ 2.58 ms$^{1}$. If u = 10, the bead comes to rest at a point D between B and C. Find (a) The greatest speed of the bead between B and D. (b) The coordinates of D. What happens after the bead reaches D? The answer for (a) is 6.83ms$^{1}$ and for (b) is (5.7, 5). Last edited by skipjack; September 3rd, 2015 at 02:49 PM. 
September 7th, 2015, 04:57 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Some hints: For the first part, use conservation of energy: the initial kinetic energy will be transferred to gravitational potential energy as it rises up the wire. KE = GPE $\displaystyle \frac{1}{2}mu^2 = mg\Delta h$ $\displaystyle \frac{1}{2}u^2 = g\Delta h$ I think you have a typo in the question as well: I think it is the speed at A which has a constraint $\displaystyle u \ge 2.58 ms^{1}$. To make this proof, consider the case where $\displaystyle v = 0$ at B. Use conservation of energy whenever you can because the equations are easier to solve than the SUVAT equations. For the second part: a) Since the only acceleration in this situation is the deceleration due to gravity, the greatest speed will be the one when the bead reaches B. Just solve a SUVAT equation to get the answer here. b) v = 0 at D... use conservation of energy again or a SUVAT equation with a little bit of trigonometry to get the horizontal and vertical distances. It should be pretty obvious what happens when the bead reaches D... Give me a shout if you're still having trouble. Last edited by Benit13; September 7th, 2015 at 04:59 AM. 
September 10th, 2015, 12:15 PM  #3 
Newbie Joined: Jun 2015 From: South Africa Posts: 27 Thanks: 0 
I'm still struggling.. no matter how i try it i still land up in a mess!

September 11th, 2015, 01:42 AM  #4 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions  

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energy, potential 
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