# Transfer of kinetic energy from a larger mass to a smaller mass

## Main Question or Discussion Point

Hello,

I'm currently a junior in high school and had an interesting idea that relates to my science fair project. If this is possible, it could create something truly innovative.

My question: Is there a way for a high mass armature's (projectile carrying device) kinetic energy to be transferred to a projectile, have the armature decelerate, and have the low mass projectile accelerate? The projectile and the armature are both moving at the same speed initially. Let's say that the mass of the armature is 4kg and the mass of the projectile is 1kg just for simplicity's sake.

My goal is to have the combined velocity of both the armature and the projectile be higher after the exchange of energy than before the exchange. Because momentum is conserved in a collision, the increase of velocity of the lower mass object should increase more than the velocity of the higher mass object decreases. Is there even a technology that can facilitate this exchange of kinetic energy? The higher the efficiency of the exchange, the better.

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If the system is closed and you are relying entirely on energy inherent in the two objects, there's no way to have the system gain energy after an event.

For instance, if you have two objects traveling towards each other, one is less massive than the other, when they impact the energy transfer is proportional to momentum. The less massive object will accelerate at a greater rate than the more massive object. The total energy within the system will either be the same, assuming 100% efficiency, or less, as the event will cause energy to be shed in forms like thermal radiation. It's essentially impossible to have 100% efficiency from an event.

In order to have a higher energy than the initial state, you must introduce energy to the system.

I hope I didn't misinterpret your plans.

After a second read, I might have actually misunderstood you. You simply want the total speed of the objects to be greater than before they collided?

You must design some impact where some of the potential energy inherent in the two objects is transformed into kinetic energy. Or that movement in an "undefined" direction is converted to velocity in the direction you desire.

For instance, a bullet is impacted by a hammer.

Or you could have two spinning objects that collide and transfer the energy from spinning into opposing acceleration. This would cause the spin rates to decrease and the opposing velocities to increase.

I understand what you are saying, but unfortunately, I think you have misinterpreted my goal. I don't want to increase the total energy of the closed system, but rather increase the total velocity.

Imagine that you have a 4 kilogram mass and a 1 kilogram mass traveling in zero gravity with a velocity of 2 m/s. The 4 kilogram mass has 8 joules of kinetic energy. The 1 kilogram mass has 2 joules of kinetic energy, for a total of 10 joules of energy in the closed system. Now, energy is transferred from the 4 kilogram mass to the 1 kilogram mass resulting in a final velocity of 1 m/s for the 4 kilogram mass (2 joules of energy) and a final velocity of 4 m/s for the 1 kilogram mass (8 joules of energy). The total energy in the system remains 10 joules. However, the total velocity, which was 4 m/s before the exchange of energy, is now 5 m/s so that the total stored energy in the system remains equal.

Is this possible?

For some reason I keep coming back to bouncy balls.

Elastic material may provide the desired effect you want. Although someone with a greater understanding of this should comment.

The armature must be low-carbon steel, and it would be preferable for the projectile to be low-carbon steel as well. All of the energy in the system will be kinetic, no rotational energy, etc. You can imagine the system as one-dimensional, if that will help. The armature will be moving at the same speed as the projectile, touching it, as they are accelerating. They will then reach a peak velocity, and stop accelerating. At that point, they both have the same velocity, and the projectile will be in front of the armature. They will probably not be touching at that point, but will be very close to each other. After that, I want to cause the armature to stop, and the projectile to gain as much of the kinetic energy from the armature as possible. Is there any technology that can do this?

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To me, that doesn't seem like a possibility as you're talking about two entirely solid objects traveling in roughly the same direction at the same speed.

Also, rotational energy is kinetic energy.

The collision (in the absolute best case scenario where no heat is produced) is governed by two equations, conservation of mechanical energy and conservation of momentum.
Cancelling out the constant term $\displaystyle{\frac{1}{2}}$ from the energy equation and setting $\displaystyle{m_2}$ as $\displaystyle{\alpha m_1}$we have
$$m_1v_1 = m_1v_1' + \alpha m_1v_2'$$
And
$$m_1v{_1}{^2} = m_1v{_1}'{^2} + \alpha m_1v{_2}'{^2}$$

So two equations with two unknowns, why don't you try solving for the two primed velocities, then see if you can find a way for them to be more than the initial velocity :)

Let me see if I understand what you are asking. Would this be the same as a large truck traveling behind a car on perfectly smooth ice, both traveling in the same direction and at the same velocity and figuring out a way to transfer all of the trucks momentum and less than or equal to total original energy to the car alone?

Yes, but instead of momentum, kinetic energy. I'm not sure if there is any way to do this in a real-world situation without large losses.

Here's the problem - you have both the objects traveling in the same direction at the same velocity. Intuitively, how will the object behind the other give the front one a push to increase its speed without using a spring or an explosion or some other way to add additional kinetic energy to the system?

And how would one accomplish this task with a lever?

Think about how a catapult works. You place the rock in end of the arm when it's under some type of tension. You release it. The potential energy that is stored while the catapult is at rest is transferred to kinetic energy of both the arm of the catapult and the rock when it's released. The arm is stopped at a point so that the trajectory of the rock will be at the desired angle so that it reaches the target BUT the rock does not increase in speed st the point when the arm of the catapult is stopped. It simply leaves the arm with the velocity the arm and rock have at the point where the arm is stopped. So there is no addition of energy to the rock from the arm when the arm is stopped. The energy of the arm is absorbed when it impacts the stopping mechanism.

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You make your heavy rock hit the short end of the lever and it will launch your light rock (at the longer end) faster. L1/V1=L2/V2

Yes you can increase the velocity of the smaller mass and its actually done in antitank missile ,where the heavier missile carry a smaller projectile ,when the missile hits an armor of a tank the smaller projectiles penetrates into the tank

Curl, I think you should read the problem again. There is no way that a lever would work in this situation.

Malemdk, antitank missiles use explosives to accelerate a smaller projectile. All of the energy in this system is kinetic energy.

I have another question. If I was able to give both the armature and the projectile a positive charge, would the repulsion cause kinetic energy to be transferred from the armature to the projectile?

Ahhh interesting.
compare this to connecting the two with an internal spring that can be released remotely. True the forces don't act the same but you can see that the spring would push backward on the large mass and forward on the smaller mass and since the force is the same and so what would happen to the accelerations? Plug some numbers in. Don't forget about conservation of momentum. Unless you have the two on a surface with a lot of friction, would it be conserved? If so you have an equation you can use for momentum and from there you can determine the amount of energy that would be transferred by a spring or the repulsion of the charges for a particular distance. From there you can also see just how much energy would be transferred from one to the other in the process. Of course the problem with using a charge is how are you going to keep it from leaking off the two objects unless they are somehow suspended. What if both objects are magnets??

Ok I see what you want.

You'll need some energy-storing device inside, like a spring, actuator, explosive, etc. Otherwise this is impossible. It's really easy to see this from newton's third law and conservation of energy.

Kinetic energy will likely not be conserved but you can calculate how much is lost or gained

Since all the real system efficiency less than 100% you cannot transfer all the energy to smaller mass ,there will be always loss in kinetic energy -it transforms in to heat- the remaining kinetic energy will be transferred the smaller mass