only need hepl on part d.

The potential energy of a particle of mass m as a function of position is given by U(.x) = U0(alpha +1/alpha), where alpha = x I alpha and a is a constant. Plot U(x) versus xfor 0.la

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To practice Problem-Solving Strategy 21.1 Conservation of energy incharge interactions.

An alpha particle (), which is the same as a helium-4 nucleus, ismomentarily at rest in a region of space occupied by an electricfield. The particle then begins to move. Find the speed of thealpha particle after it has moved through a potential difference of-3.45Ã10-3 .
The charge and the mass of an alpha particle are = 3.20Ã10-19 and =6.68Ã10-27 , respectively.

PROBLEM-SOLVING STRATEGY Conservation of energy in chargeinteractions

PREPARE Draw a before-and-after visual overview. Define symbolsthat will be used in the problem, list known values, and identifywhat you're trying to find.

SOLVE The mathematical representation is based on the law ofconservation of mechanical energy:

.

Find the electric potential at both the initial and finalpositions. You may need to calculate it from a known expression forthe potential, such as that of a point charge.
and are the total kinetic energies of all moving particles.
Some problems may need additional conservation laws, such asconservation of charge or conservation of momentum.
ASSESS Check that your result has the correct units, is reasonable,and answers the question.

Prepare
Identify the system involving the alpha particle. Then examine theforces acting within this system to determine whether mechanicalenergy is conserved. Make certain to draw a before-and-after visualoverview and to define your symbols.
Part A
Mechanical energy is conserved in the presence of which of thefollowing types of forces?
Select all that apply.
? frictional
? electrostatic
? magnetic
? gravitational

Which of the following quantities are unknown?
? the value of the electric potential at the initial position ofthe alpha particle
? the final speed of the alpha particle
? the charge of the alpha particle
? the mass of the alpha particle
? the difference in potential between the initial and finalpositions of the alpha particle
? the value of the electric potential at the final position of thealpha particle
? the initial speed of the alpha particle

An alpha particle (consisting of two protons and two neutrons), traveling at a speed of v = 1.9 x 10⁵ m/s, enters a region of constant magnetic field of strength B = 1.9 T as shown in the figure. The direction of B is out of the image. The alpha follows a path that is a circular arc of radius r.

Part (a) In atomic mass units, what is the mass m of an alpha particle?
Part (b) In units of elementary charge e, what is the electric charge q of an alpha particle?
Part (c) In meters, what is the radius of curvature r of the path taken by the alpha particle?

peachgrasshopper627

A particle of mass M is subjected to a force , where k is a constant and alpha = 0.5 s^-1. If the particle is initially at rest, calculate the position, velocity, and acceleration as a function of time.