Why does a submarine rise when its volume is increased?
a. because it now weighs less
c. because it fills with air
b. because its density is now lower than the water around it
d. because it is less buoyant when it is larger

Picture a all traveling at a constant speed around the inside of a circular structure. is the ball accelerating? explain your answer

An ideal spring has a spring constant (force constant) of 2500 n/m, is stretched 4.0 cm, how much elastic potential energy does it possess? (a) 3j (b) 0.00j (c) 1j (d) 2j (e) 4j

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.