Marble gun - how far to compress string

In summary, Brad Sue wrote that the total energy of the marble while compressed is E_i = mgh + \frac{1}{2} m v^2_y + \frac{1}{2} k x^2, and after the gun has fired is E_f = mgh + \frac{1}{2} m v_x^2 + \frac{1}{2} m v^2_y.
  • #1
brad sue
281
0
Hi, Please , take a look at this problem:
A child is trying to shoot a marble of mass m in order to hit the center of a box using a spring loaded marble gun.
The marble gun is fixed on a table and shoots the marble horizontally from the edge of the table. The edge of the table is a height h above the top of the box. The center of the box is some horizontal distance d away from the table. the spring constant is k. By what distance x should the child compress the spring so that the marble lands in the center of the box?. g is the gravitational constant.

In the solution , the manual used the conservation of mechanical energy.( I got this part).
My problem is that I don't understand why they did not use the potential energy PE=mgh
They wrote Eo=1/2*k*x2=1/2*m*v12=E1
They solved for v1, and the they used the projectile equation to find x ( by finding t)
My problem is why for the conservation of energy, they did not write:
Eo=mgh+1/2*k*x2
I saw that in other problems solutions tough!
Thank you
 
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  • #2
Hi brad sue,

You can write the total energy of the marble while compressed as
[tex]
E_i = mgh + \frac{1}{2} m v^2_y + \frac{1}{2} k x^2,
[/tex]
and after the gun has fired as
[tex]
E_f = mgh + \frac{1}{2} m v_x^2 + \frac{1}{2} m v^2_y,
[/tex]
if you want. The simplification here is that the vertical velocity [tex] v_y [/tex] (which is zero initially) and height [tex] h [/tex] don't change while the marble is being ejected from the spring gun, right? So when you equate energy before and after, the gravity term and the vertical kinetic energy term just cancel out since they haven't changed. Thus, you can leave them out in the first place if you want, but only because they don't change during the process you are considering (the initial acceleration of the ball). Make sense?
 
  • #3
Physics Monkey said:
Hi brad sue,
You can write the total energy of the marble while compressed as
[tex]
E_i = mgh + \frac{1}{2} m v^2_y + \frac{1}{2} k x^2,
[/tex]
and after the gun has fired as
[tex]
E_f = mgh + \frac{1}{2} m v_x^2 + \frac{1}{2} m v^2_y,
[/tex]
if you want. The simplification here is that the vertical velocity [tex] v_y [/tex] (which is zero initially) and height [tex] h [/tex] don't change while the marble is being ejected from the spring gun, right? So when you equate energy before and after, the gravity term and the vertical kinetic energy term just cancel out since they haven't changed. Thus, you can leave them out in the first place if you want, but only because they don't change during the process you are considering (the initial acceleration of the ball). Make sense?

Yes , it make more sense now.
What I was considering was the initial state at the top of the table, and the final state at level ground (in the box). But we needed to analyze the process of acceleration of the marble.

Thanks a lot.
 

1. What is a marble gun?

A marble gun is a type of toy gun that shoots small marbles as projectiles. It typically consists of a barrel, a trigger mechanism, and a spring-loaded plunger that propels the marble forward.

2. How do you compress the string in a marble gun?

The string in a marble gun is typically compressed by pulling back the plunger and locking it in place. This creates potential energy that is released when the trigger is pulled, propelling the marble forward.

3. How far should the string be compressed in a marble gun?

This can vary depending on the specific design of the marble gun, but a general rule of thumb is to compress the string until it is about 3/4 of the way back. This will provide enough force to launch the marble a decent distance.

4. How does the distance of string compression affect the range of a marble gun?

The distance of string compression directly affects the potential energy of the plunger, which in turn affects the force with which the marble is launched. The farther back the plunger is compressed, the more potential energy is stored and the farther the marble will travel.

5. Are there any safety precautions to take when using a marble gun?

Yes, it is important to always follow the safety guidelines provided by the manufacturer. This may include wearing protective eyewear, using the marble gun in a designated area away from people and breakable objects, and never aiming the gun at anyone or anything living.

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