Dynamics question: work and energy (spring problem)

[Superhawkkodaka]

Homework Statement

i just want everybody to check if my solution is correct.. because I am not confident with this one..
your help would be highly appreciated

Question: The 0.31kg mass slides on a frictionless wire that lies in the vertical plane. The ideal spring attached to the mass has a free length of 80mm and its stiffness is 120n/m. Calculate the smallest value of the distance b if the mass is to reach the end of the wire at B after being released from rest at A.

picture of the problem:

The attempt at a solution..
so far this is what I've done:

i think this equation of mine is wrong? or my assumptions are wrong.. since i can't solve (Sa) value using pythagorean theorem..

i don't know just my gut.. i badly need your advice guys...

 

[BiGyElLoWhAt]

Can't you just relate it through a trig function?

 

[Superhawkkodaka]

PS. i

Can't you just relate it through a trig function?

you mean for my (Sa)? there's no angle given..

 

[Quantum Defect]

1. The idea is correct, but the details are wrong.

Think about these points:

If the slider is to reach the point B, what is the critical point that it must reach? At this point, the slider's kinetic energy is zero, the energy stored in the spring is also zero. What is the energy at this point? (The height you use is incorrect.)

At the very beginning, all of the energy of the system is in the form of the potential energy stored in the spring. The resting length of the spring is 80 mm, so you need to know how much beyond 80 mm the spring has been stretched. Prof. Pythagoras can tell you how long the spring is when the slider is at B.

 

[Superhawkkodaka]

i think i got the value for Sa

correct me if I am wrong.. i thought h is the vertical distance from pt A to B from my understanding from PE=mgh

also.. critical point? I am lost i can't imagine.. why do i need to take account critical point?

all i know is that when the slider reaches point B the velocity is zero thus potential energy at B is zero since it will stop..

 

[gneill]

also.. critical point? I am lost i can't imagine.. why do i need to take account critical point?

all i know is that when the slider reaches point B the velocity is zero thus potential energy at B is zero since it will stop..

No, that's not right. The slider will have some velocity in the instant before it impacts the stop at point B. Why might that be? (where does the energy come from to give it this velocity?)

 

[Superhawkkodaka]

No, that's not right. The slider will have some velocity in the instant before it impacts the stop at point B. Why might that be? (where does the energy come from to give it this velocity?)

no velocity is given.. i think sir Quantum Defect suggestion is correct.. i already got the value Sa to solve for uknown b.. just that i think my assumed height (h = 0.08) from point A to B is wrong..

i don't know how to interpret what he said..
i'll just sir Quantum Defect quote :

Think about these points:

If the slider is to reach the point B, what is the critical point that it must reach? At this point, the slider's kinetic energy is zero, the energy stored in the spring is also zero. What is the energy at this point? (The height you use is incorrect.)

At the very beginning, all of the energy of the system is in the form of the potential energy stored in the spring. The resting length of the spring is 80 mm, so you need to know how much beyond 80 mm the spring has been stretched. Prof. Pythagoras can tell you how long the spring is when the slider is at B.

 

[Quantum Defect]

no velocity is given.. i think sir Quantum Defect suggestion is correct.. i already got the value Sa to solve for uknown b.. just that i think my assumed height (h = 0.08) from point A to B is wrong..

i don't know how to interpret what he said..
i'll just sir Quantum Defect quote :

Think about these points:

If the slider is to reach the point B, what is the critical point that it must reach? At this point, the slider's kinetic energy is zero, the energy stored in the spring is also zero. What is the energy at this point? (The height you use is incorrect.)

At the very beginning, all of the energy of the system is in the form of the potential energy stored in the spring. The resting length of the spring is 80 mm, so you need to know how much beyond 80 mm the spring has been stretched. Prof. Pythagoras can tell you how long the spring is when the slider is at B.

To get to B, the mass must reach the top of the loop, no?

 

[gneill]

Suppose you calculate the energy for the slider to reach the height at point B. How would ever reach point B? How could it pass point B' which I've marked on the figure:

 

[Superhawkkodaka]

To get to B, the mass must reach the top of the loop, no?

so the height (h) i must use is the highest point the slider have made for it(slider) to reach point B

so my height h=2(0.08)= 0.16... now i seem to be getting same answer given to us 0.15m..

ok I am just confused.. i know that the slider will reach highest point let's say "h"
why did you use the point h as reference? also why is kinetic energy zero at the highest point.. isn't that only applicable to projectile motion/free falling body problems?

isn't it point B should be your reference since it was asked for slider to reach point B? I actually used point B as my reference and assumed it's velocity is zero?

 

[Superhawkkodaka]

so the height (h) i must use is the highest point the slider have made for it(slider) to reach point B

so my height h=2(0.08)= 0.16... now i seem to be getting same answer given to us 0.15m..

ok I am just confused.. i know that the slider would reach highest point let's say "h"
why did you use the point "h" as reference? shouldn't it be at point B..

also why is kinetic energy zero at the highest point.. isn't that only applicable to projectile motion/free falling body problems? does it also apply to spring problems.. if that's the case.. if the slider reaches at "h" then it will continue to travel at point B in a free fall manner?...

 

[Quantum Defect]

The trick is to think about the actual slider. This is very much like a pinball game. You can adjust how much energy goes into the slider by stretching the spring. As the problem statement says, your goal is to find the minimume stretch (minimum energy imparted to the slider) to get the slider to B.

Imagine that you do this experimentally. You pull the slider out just a bit. The slider takes off and starts to go up the slope, but doesn't have enough energy to get to the top. You decide that you need to give the slider a bit more energy and pull the slider back a long way. The slider whips out and whirls around the loop at top speed, nearly breaking things when it hits the stop at point B. OK. You look around to make sure nobody saw you almost break the contraption. You try again with the slider pulled out between the first and second tries. On this try, the slider goes up nicely, and almost makes it over the top of the loop, and slides back down to the start. You tell yourself that you are very close. The slider needs just a tiny bit of energy more to get over the top and get to B. You pull the spring back just a bit more, and the slider goes up the loop, and at the top, the slider looks like it may be stuck, but just when you are going to push the slider back to the start, the slider starts sliding back to the left, and falls down to B.
You did it!

How did you do this? You launched it so that it had just enough energy to get to the top of the loop, with an infinitessimal amount of energy added to this to keep it moving at the very top. If you put in less energy, it will slide back to the start. If you put in too much energy, it will still have significnat kinetic energy at the top, as it whips around the loop.

Make sense?

 

[Superhawkkodaka]

The trick is to think about the actual slider. This is very much like a pinball game. You can adjust how much energy goes into the slider by stretching the spring. As the problem statement says, your goal is to find the minimume stretch (minimum energy imparted to the slider) to get the slider to B.

Imagine that you do this experimentally. You pull the slider out just a bit. The slider takes off and starts to go up the slope, but doesn't have enough energy to get to the top. You decide that you need to give the slider a bit more energy and pull the slider back a long way. The slider whips out and whirls around the loop at top speed, nearly breaking things when it hits the stop at point B. OK. You look around to make sure nobody saw you almost break the contraption. You try again with the slider pulled out between the first and second tries. On this try, the slider goes up nicely, and almost makes it over the top of the loop, and slides back down to the start. You tell yourself that you are very close. The slider needs just a tiny bit of energy more to get over the top and get to B. You pull the spring back just a bit more, and the slider goes up the loop, and at the top, the slider looks like it may be stuck, but just when you are going to push the slider back to the start, the slider starts sliding back to the left, and falls down to B.
You did it!

thanks dude!. took me long enough to realize. it's just me being slow learner.. hehe.. thanks to all who helped me guys..
How did you do this? You launched it so that it had just enough energy to get to the top of the loop, with an infinitessimal amount of energy added to this to keep it moving at the very top. If you put in less energy, it will slide back to the start. If you put in too much energy, it will still have significnat kinetic energy at the top, as it whips around the loop.

Make sense?