Consider the formula d=\dfrac{m}{v}d= v m d, equals, start fraction, m, divided by, v, end fraction, where ddd represents density, mmm represents mass and has units of kilograms \left( \text{kg}\right)(kg)left parenthesis, k, g, right parenthesis, and vvv represents volume and has units of cubic meters \text{(m}^3)(m 3 )left parenthesis, m, start superscript, 3, end superscript, right parenthesis. select an appropriate measurement unit for density.

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 electric field direction is defined by the direction of the force felt by (select one of the following answers): 1. a negative charge. 2. a positive charge. 3. both positive and negative charges.

Consider the growth of a 20-nm-diameter silicon nanowire onto a silicon wafer. the temperature of the wafer surface is maintained at 2400 k. assume the thermal conductivity of the silicon nanowire is 20 wm-1k-1 and all its surfaces including the tip are subjected to convection heat transfer with the coefficient h = 1×105 wm-2k-1 and t∞ = 8000 k. when the nanowire grows to l = 300 nm, what is the temperature of the nanowire tip (t (x =