Aforce in the +x-direction with magnitude f(x)=18.0n−(0.530n/m)x is applied to a 8.40 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. f(x) is the only horizontal force on the box. so, if the box is initially at rest at x=0, what is its speed after it has traveled 16.0 m? express your answer to three significant figures and include the appropriate units.

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.

A100 kg running back runs at 5m/s into a stationary linebacker. it takes 0.5 for the running back to be completely stopped

A0.580-kg rock is tied to the end of a string and is swung in a circle with a radius of 0.500 meters. the velocity of the rock is 4.50 m/s. what is the centripetal force acting on the rock? 15.5 n 5.22 n 69.8 n 23.5 n