# Why does a perpetual motion machine of the first kind violate the law of conservation of energy?

For it to function, energy must be created.

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one type to another. A perpetual motion machine of the first kind produces work without the input of energy. Therefore, the output is larger than the input.

The internet is full of videos purporting to show a perpetual energy machine in action, but those are fake. If the videos went on, you would see the machine slow down and eventually stop because of the friction operating on the system. Additionally, if the machine was intended to drive some load, like lifting a mass, it would stop sooner or even sooner.

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A perpetual motion machine of the first kind violates the law of conservation of energy because it claims to produce energy indefinitely without any external input, which contradicts the principle that energy cannot be created or destroyed, only transformed from one form to another.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A force field is described by #<F_x,F_y,F_z> = < xy , xy-x, 2y -zx > #. Is this force field conservative?
- A spring with a constant of #12 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #6 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A ball with a mass of #144 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #6/4 m# when the ball was released. How high will the ball go?
- A wagon is pulled at a speed of 0.40 meters/sec by a horse exerting an 1,800-newton horizontal force. What is the power of this horse?
- A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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