In separate experiments, four different particles each start from far away with the same initial speed and impinge directly upon the nucleus of a gold atom. The masses and charges of the particles are:

particle 1: mass m, charge q.
particle 2: mass 2m, charge 2q.
particle 3: mass 2m, charge q/2.
particle 4: mass m/2, charge 2q.

Rank the particles according to the distance of closest approach to the gold nucleus from smallest to largest.

a. 1,2,3,4
b. 4,3,2,1
c. 3, 1 and 2 tie, 4
d. 4, 1 and 2 tie, 3
e. 1 and 2 tie, 3, 4

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Quantum mechanics applies to subatomic, atomic, nanometer-size, and micrometer-size systems. nanometer, micrometer, and kilometer-size systems. atomic, nanometer-size, and micrometer-size systems. subatomic, atomic, and nanometer-size systems.

This is important. 1. which of the following is an si base unit for measuring length? (2 points) inch gram meter mole 2. which of the following units for distance is an si unit? (2 points) centimeter foot inch yard 3. which of the following tools should a scientist use to measure an object in meters? (2 points) electronic balance pan balance tape measure thermometer