A series of four different cylinders were each subjected to a force by placing four different masses on top of them. The mass placed on each cylinder and dimensions of each cylinder are shown below. Rank the stress on these cylinders from least to greatest.
Mass (kg) Diameter (cm) Height (cm)
Case
A
B
С
D
5.2
3.6
4.7
2.9
2.6
2.3
2.7
32.2
32.5
27.3
16.9

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.

The difference between a red shift and a blue shift has to do with wavelength frequency. t or f

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?