Which of the following cannot be determined from the spectrum of a star? the temperature of the atmosphere of the star
the motion of the star
the chemicals in the atmosphere of the star
the chemicals in the core of the star

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.

Consider a 1000 w iron whose base plate is made of 0.5 cm thick aluminum alloy 2024-t6 (ρ = 2770 kg/m3 and cp = 875 j/kg°c). the base plate has a surface area of 0.03 m2. initially, the iron is in thermal equilibrium with the ambient air at 22°c. assuming 90% of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 200°c.

Amachinist turns the power on to a grinding wheel, at rest, at time t = 0 s. the wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. the wheel is run at that angular velocity for 40 s and then power is shut off. the wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. in this situation, the time interval of deceleration is closest to: