3. How much mass would a 10-9 sample of gold have on Uranus, with a gravity of 8.7 m/s2? 8.7 N
1.159
870 N
10 9

Aprojectile is launched horizontally 10m above the ground and with an initial velocity of 15 m/s. a) determine the magnitude and direction of projectile velocity at t= 1.3s b) determine the magnitude and direction of projectile acceleration at t=1.3s

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.

An ideal gas is held in a container at constant volume. initially, its temperature is 5 degrees c and its pressure is 1.2 atm. what is its pressure when its temperature is 43 degrees c? answer in units of atm