Question

A Slingshot with a force constant of890N/m is used to propel a primitive 10 005kg starship into deep space by releasing a 5kg block of ice into space. How much should the slingshot be pulled in order to increase the ships speed by 5m/s? (unit is Gravitational potential energy)

Answer 1

i didn't understand the significance of the kg block can you please explain me??

Answer 2

neither do I, sorry

Answer 3

okay i'll try to get it!

Answer 4

the answer is 17m if that helps

Answer 5

oh! i got that
this is momentum conservation

Answer 6

just one moment:)

Answer 7

i'm trying it...

Answer 8

i think energy conservation may be involved in this

Answer 9

lol i'm getting (94)^1/2

Answer 10

yes

Answer 11

?

Answer 12

i'm trying it even now this is damn good!

Answer 13

yes, i know, im having difficulty figuring out what to start with :/

Answer 14

what are you trying first? which equations?

Answer 15

look i think we need to use two equations
one is the equation for momentum conservation and another is th work energy theorem
i think so!

Answer 16

can we assume that the initial velocity of the starship is stationary?

Answer 17

no

Answer 18

Hello both of you!

You are right, it is conservation of momentum and something more.

Answer 19

Hello

Answer 20

if we use these two equations , we can get the initial and the final velocities seperately
i mean i got it seperately

Answer 21

hello

Answer 22

Speed is increased 5 m/s, so velocity may be different than zero

Answer 23

yeah!

Answer 24

doesn't the spring constant come into play too? would the equation \[F=Kx\] come into play?

Answer 25

F= kx is necessary, good point

Answer 26

i used these equations and the masses were so large that it was very hard to solve it so i took the help of an online calculator
and the spring may come into the story in the work energy theorem or ..

Answer 27

if we find force then we can find x, but im unsure how to find force

Answer 28

but if we use momentum conservation , we will not get any term that would include force and the spring force is an internal force (due to which we can apply momentum conservation)

Answer 29

You can calculate how much momentum of space ship
Increases, but energy needs another equation.

Answer 30

i didn't get that:)

Answer 31

Momentum p =mv, both spaceship and ice block have same momentum,
At the beginning p = 0.

Answer 32

oh i got it now!

Answer 33

I think rajat is working with energy.

Answer 34

yes i am
i'm actually working with both
momentum conservation and energy conservation
because according to my solution , i got two variables in n equaiton so i need both the equations
what do you think?? is it right??

Answer 35

Looks good, go on. This is somehow similar as radioactive decay.
Kinetic energies of spaceship and ice block give energy equation.

Answer 36

i think i got something..

Answer 37

no i got nothing!

Answer 38

Sorry, I have to log out, but go on working.
I'll fan both of you, so lets keep in touch.
But don't medals to me, nikkii, rajat did the work!

Have a nice day!

Answer 39

you helped us
thanks a lot for giving your time for the question

Answer 40

and have a nice day!

Answer 41

THank you for your time!

Answer 42

\[m _{1}v _{1o} + m _{2}v _{2o} = m _{1}v _{1f} + m _{2}v _{2f}\]

\[\frac{ 1 }{2 } m _{1}v _{1o}^{2} + \frac{ 1 }{2 } m _{2}v _{2o} ^{2}= \frac{ 1 }{2 } m _{1}v _{1f}^{2} + \frac{ 1 }{2 } m _{2}v _{2f}^{2}\]

Answer 43

are these the 2 equations you are using?

Answer 44

the first one is correct and the second one is also correct but we need to bring the work done by the spring somewhere in the picture
and these equations are absolutely correct!

Answer 45

i'll try this one and get you on that in just 15 minutes:)

Answer 46

thank you

Answer 47

thanks for fanning me!

Answer 48

no probs!

Answer 49

I just remember that potential energy of the slingshot is
E = 0.5kx^2. It is shared to spaceship and ice block.

Can you calculate speed of the ice block?

Answer 50

initial or final?

Answer 51

how does that equation relate to speed?

Answer 52

First ice block is moving with the spaceship, if it is moving.
You know change of momentum of spaceship.
It get 5 m/s speed more.
Ice block is lighter, so it's speed is higher, and it comes
From conservation of momentum

Answer 53

what equation do we use to find change in momentum? we don't know the initial velocities or the final one of the ice block. Since the ice block is being released, would we get two different momentum's that add up to the original?

Answer 54

Change of momentum of spaceship is
p1= mv = 10005 kg * 5 m/s

Then speed of ice block after slingshot is v2 = p1/ 5 kg

Answer 55

what i did is i kept in mind the fact that internal forces cannot change the momentum of the system but they can change the kinetic energy of the system
so i think the equation that nikkiii made for energy conservation needed something additional and that is the potential energy of the spring.

Answer 56

how did you get the equations v2= p1/5kg?

Answer 57

and wouldnt that be p2? since p2=mv=10005kg * 5m/s.
We don't have the initial velocity of the starship yet

Answer 58

Conservation of energy:
Potential energy of slingshot = kinetic energy of spaceship + kinetic energy of ice block
Problem is that kinetic energy is not shared equally.

Answer 59

i wrote the momentum conservation equation as follows:
let v1 be the speed of the spaceship initially
so pi=10005v1
finally, i assumed the speed of the ice block to be v2 so the final momentum was
pf=10000(v1 + 5)+5v2 (velocity of the 10000kg spaceship increases by 5m/s)
so do you think that this is correct??

Answer 60

Before slingshot situation is similar as in a gun.
When a bullet has high speed, gun has a smaller recoil speed.
Whether spaceship is moving or not before slingshot
effect, is not important when working with momentum

Answer 61

okay!

Answer 62

i gotta go it's too late for me
bye join you tomorrow:)

Answer 63

bye

Answer 64

According what rajat wrote, change of momentum is pf - pi

But, let's continue tomorrow, I try to think this, too

Bye to both of you, you were working hard.

Answer 65

Bye!

Answer 66

Hello , nikkii and rajat!

I thought slingshot applies same force to spaceship and ice block.
Forces are equal according the law of for action and reaction (Newton III law)

Then W= Fx (work done by slingshot)
We get W = 0,5kx^2

Then work done by slingshot is change of kinetic energy...

I got 0.5kx^2 = 0.5mv^2

When you solve x, it is 16.76 m, could that be so simple?

Maybe we thought this too difficulty

Answer 67

Hey! and we were probably over analyzing it. Thank you Geboors!

Answer 68

that really makes sense!
you rock @Gebooors