Show by direct computation that the impulse momentum theorem and the work-energy theorem are invariant under the Galilei transformation.

Three point charges, q, 2q, and 3q, are at the vertices of an equilateral triangle of sides a. If q= 15.8 nC and a= 11.1 cm, what is the magnitude of the electric field at the geometric center of the triangle?

Please explain in details, in particular the trig to set up the equilateral triangle. I am confused.

A 2000-kg car is traveling at 20 m/s on a horizontal road and the engine suddenly is broken down. The brakes immediately are applied and the car skids to a stop in 4.0 s with a constant acceleration because of kinetic friction. What is the coefficient of kinetic friction between the tires and road?

Why was it unnecessary to connect the ground alligator clip in the Oscilloscope experiment

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.658 of the escape speed from Earth and (b) its initial kinetic energy is 0.658 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

Consider a finite square well, with V = 1.2 eV outside. It holds several energy states, but we are only interested in two:

• E₁ = 1.15 eV
• E₂ = 1.1 eV

1) For E = 1.15 eV, what is the decay constant, κ, outside the well in nm^-1(i.e., where V = 1.2 eV)?

κ =

2) For E = 1.1 eV, what is the decay constant, κ, outside the well in nm^-1 (i.e.,) where V = 1.2 eV)?

κ =

3) For E = 1.15 eV, suppose the probability density at some position,x, outside the well is P(x) and the probability density 1 nm farther from the well is P(x+1 nm). What is the ratio, P(x+1 nm)/P(x), of these two probailities?

Ratio =

4) For E = 1.1 eV, suppose the probability density at some position,x, outside the well is P(x) and the probability density 1 nm farther from the well is P(x+1 nm). What is the ratio, P(x+1 nm)/P(x), of these two probailities?

Ratio =

5) If we squeeze the well (decrease L), the energies of the states will increase. What is the limiting value κ_limit of an energy state's κ as its energy approaches the top of the well in nm^-1(i.e., as E → 1.2 eV).

κ_limit =

Question 2: You want to determine if there are any Kuiper Belt objects larger than Eris.

Part a: Describe the observational methods and analysis you would apply to search for them.

Part b: How might you determine if any candidate objects are larger than Eris? What observational data do you need for an object to estimate its radius?

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r, and a hollow cylinder of radius r are all allowed to roll down an incline. Derive a general relationship for the linear acceleration of each object depending on the angle of the ramp and the rotational inertia. You may assume that the frictional force is small enough that it is only causing rotation in each case.

Resistors connected in series generally always

select all that apply