A 700-kg elevator starts from rest. It moves upward for 4.50 s with constant acceleration until it reaches its cruising speed of 1.75 m/s. (a) What is the average power of the elevator motor during this time interval?

There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.2 cm38.2 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0705 NF1=0.0705 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 NF2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2k=1/(4πϵ0)=8.99×109 N⋅m2/C2 .

James has just jumped out of an airplane. After he opens his parachute he experiences 2 forces: the constant force of gravity, and a wind drag that is proportional to his velocity. His height may therefore follow the equation: d²h/dt² = -9.8 - 2(dh/dt). As a second-order differential equation, this is not technically solvable by separation of variables. However, because the variable h appears only in its derivatives, we can turn this into a first-order equation, and solve that by separation.

a) Letting v = dh/dt, rewrite the above equation as a first-order differential equation in v.

b) Your equation in part a suggests that there is one velocity for which dv/dt = 0. What is this velocity?

c) Solve your equation using separation of variables. Your solution should contain an arbitrary constant: call it C₁.

d) Calculate lim t to infinite v(t) and use it to describe what is physically happening to James after he's been in the air for a long time.

e) Now that you have a velocity function v(t), integrate it with respect to t to find a position function h(t). This will introduce a second constant C₂.

f) Suppose James begins at a height of 3000m with no initial velocity, what is his height 3s later?

A dielectric-filled capacitor consists of two parallel plates, each with an area  A = 15.0 cm2 , seperated by a distance of d = 10.0 mm and dielectric constant k = 4.00. A potential difference  V= 10.0 V  is applied to these plates . Throughout the problem, use ϵ0 = 8.85×10⁻¹² C2/N⋅m2

Part A)

Calculate the energy U1of the dielectric-filled capacitor.(J)

Part B)

The capacitor remains connected to the battery. Calculate the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric, because the dielectric is slowly pulled away. of(J)

Part C

The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3 of (J)

Part D)

In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric? of (J)

t² (d²r/dt²) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation." Such equations appear in a number of physics and engineering applications.

a) Write the complementary homogeneous equation.

b) Plug r = e^kt into the equation you wrote in part a. Show that this solution will not work for any constant k: this equation has no exponential solution.

c) Plug the guess r = tⁿ (where n is a constant) into the equation you wrote for part a. Solve the resulting algebraic equation for n; you should find 2 solutions.

d) Write the general solution to the equation you wrote in Part a.

e) Find a specific solution to the origianl (inhomogeneous) equation.

f) Write the general solution to the inhomogeneous equation.

g) What is it about this particular equation that made r = tⁿ work?

make technology papers related to scattering

Over and over I'm getting into the same trouble, so I'd like to ask for some help.

1. I need to solve some basic electrodynamics problem, involving magnetic fields, moving charges or currents.
2. But I forgot all this rules about "where the magnetic field should go if the current flows up". I vaguely remember that it about hands or fingers or books or guns, and magnetic field should go somewhere along something, while current should flow along something else... But it doesn't help, because I don't remember the details.
3. I do find some very nice rule and use it. And I think "that one I will never forget".
4. ...time passes...
5. Go to step 1.

The problem is that you have to remember one choice from a dichotomy: "this way or that way". And all the mnemonics I know have the same problem -- I got to remember "left hand or right hand", "this finger or that finger", "inside the book or outside of the book".

Maybe someone knows some mnemonics, that do not have such problem?

make technology papers related to potential variations

Which is larger, an increment of 1°C, or of 1°F? Explain, using an example if needed.

An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 24.0% of its original volume and the temperature is increased to 48.0°C.

(a) What is the tire pressure in pascals?
Pa

(b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 3.00%. What is the new tire pressure (absolute) in pascals?
Pa

A mass m = 16 kg is pulled along a horizontal floor with NO friction for a distance d =8.4 m. Then the mass is pulled up an incline that makes an angle ? = 25

1. When a glass rod is rubbed with silk, it
(a) gains electrons from silk.
(b) gives electrons to silk.
(c) gains protons from silk.
(d) gives protons to silk.

2. In general, metallic ropes are suspended on the carriers taking inflammable materials. The reason is
(a) to control the speed of the carrier.
(b) to keep the centre of gravity of the carrier nearer to the earth.
(c) to keep the body of the carrier in contact with the earth.
(d) none of these.

3. Two similar spheres having +Q and -Q charges are kept at a certain distance. F force acts between the two. If at the middle of two spheres, another similar sphere having +Q charge is kept, then it experiences a force in magnitude and direction as
(a) zero having no direction.
(b) 8F towards +Q charge.
(c) 8F towards -Q charge.
(d) 4F towards +Q charge.

4. A charge Q is divided into two parts of q and Q – q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of Q/q should be
(a) 2:1
(b) 1/2
(c) 4:1
(d) 1/4

5. Two charges of equal magnitudes kept at a distance r exert a force F on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is

a)f/8

b)f/4

c)4f

d)f/16

6. The electric field inside a spherical shell of uniform surface charge density is
(a) zero.
(b) constant, less than zero.
(c) directly proportional to the distance from the centre.
(d) none of the these

7. A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

8. Electric field at a point varies as r° for
(a) an electric dipole
(b) a point charge
(c) a plane infinite sheet of charge
(d) a line charge of infinite length

9. The electric field intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance rir r(r > R) from its axis is
(a) directly proportional to r².
(b) directly proportional to r³.
(c) inversely proportional to r.
(d) inversely proportional to r².

10. The magnitude of electric field intensity E is such that, an electron placed in it would experience an electrical force equal to its weight is given by
(a) mge
(b) mg/e
(c) e/mg
(d) e²g/m²

PLEASE TYPE THE ANSWER

As simply as you can but with complete and comprehensive detail, state and explain each of Newtons Three Fundamental Laws of Motion. After you have explained all Three Laws look through the example problems given in the book and come up with and explain an example problem of your own. It must include an explanation of how at least one of Newton's laws is used if not more than one.

A blue ball is thrown upward with an initial speed of 22.2 m/s, from a height of 0.5 meters above the ground. 2.7 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 10.7 m/s from a height of 26.9 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s²

^a. What is the height of the red ball 3.51 seconds after the blue ball is thrown?

b. How long after the blue ball is thrown are the two balls in the air at the same height?

c. Which plot correctly shows the velocity of the two balls as a function of time?

d. Which statement is true about the blue ball after it has reached its maximum height and is falling back down?

The acceleration is positive and it is speeding up

The acceleration is negative and it is speeding up

The acceleration is positive and it is slowing down

The acceleration is negative and it is slowing down

1. What happens when a spinning ice skater draws in her outstretched arms? (a) her angular momentum decreases (b) her angular momentum increases (c) her rotational speed decreases (d) her rotational speed increases