How does the pKa values of an ionizable side chain compare when the amino acid is free versus when it is in a polypeptide chain?

Avoltage source vs = 10 v is in series with a resistor of 10 kohm. if the source transformation theorem is applied, what will the value of the current source be in ma ?

A500g object falls off a cliff and losers 100 j from its gravitational potential energy store. if the gravitational field strength g=9.8n/kg, how high is the cliff?

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.