A 20-kg object sitting at rest is struck elastically in a head-on collision with a 10-kg object initially moving at 3.0 m/s. Find the final velocity of the 20-kg object after the collision. -1.0 m/s -2.0 m/s 1.5 m/s 2.0 m/s

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.

1.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the mass defect of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev 2.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the binding energy of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev 3.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the binding energy per nucleon of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev

The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?