Velocity of a cork fired from a cork gun

[esoteric deviance]

A spring is compressed by 5.5 cm and used to propel a 3.8 g cork from a cork gun. k = 10 N/m.

A) What is the speed of the cork if it is released as the spring passes through its relaxed position?

B) Suppose, instead, that the cork sticks to the spring and stretches it 1.5 cm before separation occurs. What now is the speed of the cork at the time of release?


For part A, I used the law of conservation of energy to get:

KE of the cork = PE of the spring​

(1/2)m(v^2) = (1/2)k(x^2)​

v = 2.82 m/s​

But for part B, I'm not sure what to do .
I know I need to use conservation of energy again, but I don't know how to set it up.

 

[radou]

Hint: if the spring streches, it has an amount of potential energy stored in it.

 

[esoteric deviance]

Still don't know what to do lol.

Unfortunately, I might need a bit more than a hint on this one.
Sadly, I've been trying to figure it for the past 45 min to no avail :(.

Maybe if you could show me how to set up the conservation thing and explain the reasoning behind it...

 

[radou]

Well, what does 1/2 k x^2 represent?

 

[esoteric deviance]

the PE of the spring when it's compressed?

 

[radou]

the PE of the spring when it's compressed?

Right, when it's compressed and when it's streched.

 

[esoteric deviance]

but wouldn't the values be different since the change in x when it's compressed is 5.5 cm and the change in x when it's stretched is 1.5 cm?

 

[turdferguson]

The EPE initial (KE=0) = the combination of EPE and KE at any point. The problem would be the same whether the string was compressed 1.5 cm or stretched

 

[radou]

but wouldn't the values be different since the change in x when it's compressed is 5.5 cm and the change in x when it's stretched is 1.5 cm?

Yes, the values are different, and there is no problem here. Define two points. One is the point when the spring is compressed by 5.5 cm, and the other is the point when the spring is streched by 1.5 cm. Define energy (sum of kinetic and potential energy) for both of these points. Now set these energies equal (since energy is conserved), and solve for v.

 

[esoteric deviance]

the thing is that I'm not sure how to do that.

is it something like

KE of the cork = final PE of spring - initial PE of spring?​

 

[radou]

the thing is that I'm not sure how to do that.

is it something like

KE of the cork = final PE of spring - initial PE of spring?​

Point 1: the spring posesses potential energy, the cork posesses no energy.

Point 2: the spring posesses some other potential energy, the cork posesses kinetic energy.

Energy at point 1 = Energy at point 2.

 

[esoteric deviance]

so these are the points right|-----5.5 cm-----|--1.5 cm--|
1 2

(that 2 should be at the end of the line)

point 1 = initial
point 2 = final

so i get:
initial PE of spring + initial KE of cork = final PE of spring + final KE of cork

is that right?

 

[radou]

Yes, that is right. The 'initial' KE of the cork equals zero, of course. Now plug in the numbers and solve for v.

 

[esoteric deviance]

thanks