PLEASE HELP! If a load of 30N causes an extension of 60cm, what load is required for an extension of 50cm?

What happens to the velocity of the car when the upward pull of the cable is greater than the downward pull of gravity as the car rises toward the top?

How many seconds does it take a pebble released from rest off a bridge to fall 29.4 m ? what is the pebble's speed when it has fallen 29.4 m ?

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.