# Conservation of energy for toy gun

• WY
In summary, this situation involves a toy gun that shoots a ball up in the air. There is no air resistance, so the ball never touches the inside of the gun. The ball reaches a maximum height h_max (measured from the equilibrium position of the spring) after being released. The spring has a constant k, and the gravitational potential energy (near the Earth's surface) is given by mgh. The spring potential energy is given by 1/2 k x^2, and it is inversely proportional to both the Earth's gravitational constant and the mass of the object shot up.
WY
I've been reading about a situation on the conservation of energy:
A spring-loaded toy gun is used to shoot a ball of mass m straight up in the air. View Figure The spring has spring constant k. If the spring is compressed a distance x_0 from its equilibrium position and then released, the ball reaches a maximum height h_max (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume x_o is greater than h

Now my question to this is that:
Is mechanical energy conserved because no nonconservative forces perform work on the ball and do nonconservative forces act in this situation after the ball is released at all? and do the forces of gravity and the spring have potential energies associated with them?

As you can tell I don't really have a great grasp on these concepts, so would anyone like to enlighten me please? thanks so much!

WY said:
Now my question to this is that:
Is mechanical energy conserved because no nonconservative forces perform work on the ball and do nonconservative forces act in this situation after the ball is released at all?
No nonconservative forces act on the ball at any time (in this problem). That's why they specify "There is no air resistance, and the ball never touches the inside of the gun."; those would be nonconservative forces.

and do the forces of gravity and the spring have potential energies associated with them?
Absolutely. Gravitational potential energy (near the Earth's surface) is given by $mgh$, where "h" is height measured from some arbitrary reference point. Spring potential energy is given by $1/2 k x^2$, where x is the displacement from the unstretched position.

so, h,max=(1/2)kx^2/gm
look closely at this equation and it will make sense to you!
the stiffer the spring the larger the "k" the more energy the spring has when it is compressed, and the higher the ball will go for a given x the distance the spring is compressed! A springs potential energy stored is proportional [1/2 k] to its distance compressed squared.
and inversely proportional to both the Earth's gravitational constant and the mass of the object shot up!

this should make some sense, right?

love and peace,
and,
peace and love,
(kirk) kirk gregory czuhai
http://www.altelco.net/~lovekgc/kirksresume.htm

Last edited by a moderator:
Kirk,

"A springs potential energy stored is proportional [1/2 k] to its distance compressed squared. and inversely proportional to both the Earth's gravitational constant and the mass of the object shot up! this should make some sense, right?"

Actually no.

What does "the Earth's gravitational constant" or "the mass of the object shot up" have to do with a spring's potential energy?

## What is conservation of energy?

The conservation of energy is a fundamental principle in physics that states energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

## How does conservation of energy apply to toy guns?

Conservation of energy applies to toy guns in the same way it applies to any other object. When a toy gun is fired, the potential energy stored in the spring or elastic band is converted into kinetic energy, propelling the projectile forward.

## Why is conservation of energy important for toy guns?

Conservation of energy is important for toy guns because it ensures that the gun will perform consistently and accurately every time it is fired. Without the conservation of energy, a toy gun may not have enough energy to launch the projectile or may have too much energy, causing potential safety hazards.

## What factors affect the conservation of energy in toy guns?

The conservation of energy in toy guns is affected by factors such as the type of mechanism used (spring, elastic band, air pressure), the weight and design of the projectile, and external forces such as air resistance or friction.

## How can we increase the conservation of energy in toy guns?

To increase the conservation of energy in toy guns, we can use more efficient mechanisms, reduce the weight of the projectile, and minimize external forces. We can also use materials that have high elastic potential energy, such as rubber, to increase the amount of energy stored in the toy gun.

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