A 100-g aluminum calorimeter contains 500 g of water at a temperature of 20ºC. Then a 140-g piece of metal, initially at 344ºC, is added to the calorimeter. The metal, water, and calorimeter reach an equilibrium temperature of 32ºC. What is the specific heat capacity of the metal? The specific heat capacity of aluminum is 910 J/kg ∙ K, and of water is 4190 J/kg ∙ K.

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.

According to newtons universal law of gravitation, which would change the parh of the ball so it traces out widest curved path possible?

Starting with only the balmer series light (visible light), how could we ensure that the solar panels generate a current that mark can use for his power station? a)by gradually increasing the brightness (amount) of light that we shine on it. b)by gradually increasing the frequency of the light we shine on it. c)by gradually increasing the wavelength of the light that we shine on it.