Calculating Spring Gun Ball Speed with Negligible Friction | Homework Help

[makeAwish]

Homework Statement

In a spring gun, a spring of mass 0.244kg and force constant 3500N/m is compressed 2.00cm from its unstretched length. When the trigger is pulled, the spring pushes horizontally on a 4.1×10−2kg ball. The work done by friction is negligible. (a) Calculate the ball's speed when the spring reaches its uncompressed length ignoring the mass of the spring.

ans is 5.8m/s ( i got this answer correct, but there is a second part of the qns which i can't solve)

part b: Calculate the ball's speed when the spring reaches its uncompressed length including, using the results of part A, the mass of the spring.

Homework Equations

(K + Ug + Ue) initial = (K + Ug + Ue) final

The Attempt at a Solution

i tried by just replacing the mass in part a with their total mass. I got 2.1m/s but it is incorrect.


Thanks!

 

[makeAwish]

the thing is i don't quite understand how to use results of part a.
means i have to use 5.8m/s to form eqn to solve?

 

[Delphi51]

Interesting! Looks like they want you to consider that part of the spring energy goes into the KE of the spring itself, leaving a bit less for the ball, so you will get a smaller answer in b. I'm thinking spring E -> KE of spring + KE of ball

As a first go at it, you might just put a 1/2mv^2 for the KE of the spring.
That isn't quite right, because one end of the spring is tied down and doesn't move.
There is another thread going tonight on just this problem. Oh - it's one of yours!

 

[makeAwish]

oh. so i cannot replacing the mass in part a with their total mass? like consider both as a system?

 

[makeAwish]

then does the spring has potential energy as well?

 

[makeAwish]

OH. i know le.. my mistake. sorry.. part a is not referring to this qns one. It is referring to just now the other qns that u helped me solve. Haha. Sorry.

 

[Delphi51]

Adding the spring and ball mass would be assuming the whole spring is moving - not quite right. If this is from the same class as your other problem about the spring with mass, you probably should use that result here. Did you find that the KE of the spring was 1/6*m*v^2 ?

 

[makeAwish]

yup. i tried this:

1/2kx^2 + (mass of ball + mass of spring)*g*x = 1/2*mass of ball*velocity of ball^2 + 1/6*mass of spring*velocity of ball^2

velocity of ball and spring is the same rite?

 

[makeAwish]

i got my answer as 3.25m/s but the ans is 3.4m/s.. hmm.

 

[Delphi51]

What is the (mass of ball + mass of spring)*g*x for?
The problem is horizontal, so no change in potential energy. You could add it to both sides, but no point.

 

[makeAwish]

What is the (mass of ball + mass of spring)*g*x for?
The problem is horizontal, so no change in potential energy. You could add it to both sides, but no point.

ya hor! haha. thanks thanks! means my first one - velocity of ball also wrong lei.. cos i included potential energy for that. but i still got the answer.. lol. i try again.

 

[makeAwish]

ok yup the answer is the same. haha. thanks for the guidance!

 

[Delphi51]

Most welcome! It may seem like drudgery, but it is really EXPERIENCE.
If you have time (unlikely) read "Outliers" by Malcolm Gladwell. He says a person's skill depends almost exclusively on experience and it takes 10 000 hours to become a world class expert.