An m = 8.09 kg mass is suspended on a k = 473000 n/m spring. the mass oscillates up-and-down from the equilibrium position yeq = 0 according to y(t) = a sin(ωt + φ0). calculate the angular frequency ω of the oscillating mass. answer in units of s−1 . question 3, chap 15, sect 3. part 2 of 4 10 points at time t0 = 0 the mass happens to be at y0 = 4.05 cm and moving upward at velocity v0 = +4.12 m/s. (mind the units! ) calculate the amplitude a of the oscillating mass. answer in units of cm.

You carry a 7.0-kg bag of groceries 1.2 m above the ground at constant speed across a 2.7m room. how much work do you do on the bag in the process? (a) 157j (b) 0.00j (c) 185j (d) 82j

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.

How does the amount of energy required to hold each proton and neutron in the nucleus compare to the energy released when they are removed?