The change in gravitational potential energy is mg(L-h).That means this is the minimum mechanical energy it would take. In reality, takes us more than this because our bodies are not perfectly efficient at using energy.

Hope this helps!

By conservation of energy, if mechanical energy is being "used up," it is being transformed into another kind of energy. Here, that is gravitational potential energy, so mechanical energy is being used at the same rate as potential energy is increasing.

Since this is U= mgh, you need to use the given quantities to find the rate that mgh is changing. [HINT: The car's mass (m) and the gravitational field (g) are not changing!]

This is a very hard question to answer, but a good one if you are confused. Energy is an object or system's ability to do work or to make things happen. It can be stored in different ways (mass, light, chemical bonds) and gets transformed by different processes.

You are probably aware that "You need energy to do things." I wish I could give you a better, non-circular answer to "What is energy?" than "It's what you need to do things," but this is really the best I can offer. Energy is not a concrete thing, but an abstract idea.

The mass of a Hydrogen atom is Mass(proton)+ Mass(electron) - Binding Energy. You will need to find the ratio of the mass of the proton and electron to the hydrogen atom.

The derivation of the parallel axis theorem is a google search away, however I may be able to relate the basic idea to you.

Moment of inertia equations are found by integrating over an object.

The moment of inertia about to the z axis is

which becomeswhich is+ 0

Hope this helps!

Remember that angular momentum of a particle is: L= r x p. The result of both the position and momentum being in the x-y plane is that the angular momentum is completely in the z-direction

The effect of a magnetic field on a charged particle is to apply a force:

F = q v B sin θ

where θ is the angle between the velocity and the magnetic field. You know that in a conductive wire, electrons can flow as current. If there is an external magnetic field perpendicular to the wire (θ = 90 degrees), the electrons will experience a force that sends them towards one side of the wire. Notice that the force law contains the charge q -- in other words, negative charges will experience a force opposite that of positive charges. The result is that negative charge will build up on one side of the wire, and positive charge on the other.

This division of charge creates essentially a capacitor, which you know creates an electric field and thus a voltage difference from one side of the wire to the other. The result is that by measuring the Hall effect we can measure the density of charge carriers, determine whether positive or negative charges are flowing, and measure the strength of magnetic fields.

A charged particle moving in a uniform magnetic field will travel in a circle -- this is the cyclotron effect. The formula for the cyclotron radius is

r = mv/qB

See if you can use that to find the speed v.

Isotopes differ in the number of neutrons, so their masses are different. The names of the isotopes tell you the mass number, so if you are given the mass of one you should be able to compute the mass of the other isotope. Neutrons are electrically neutral, meaning that they don't affect the charge of the isotope. From this information you should be able to use the formula for the cyclotron radius.

The Brewster's angle gives us the following relationship: the incident angle plus the refracted angle equals 90 degrees. You can write this as a simple equation to find the incident angle, then you can use Snell's law to find the the index of refraction of the glass.