A race car rounds one end of a speedway. This end of the track is a turn with a radius r of approximately 187 ft. If the track is assumed to be completely flat and the race car is traveling at a constant 60.00 mi/h around the turn, what is the race car's centripetal (radial) acceleration a c ? a c = 41.41 ft / s 2 Convert this result to SI units. a c = 12.621768 m / s 2 What is the force responsible for the centripetal acceleration in this case? gravity weight friction normal To keep from skidding into the wall on the outside of the turn, what is the minimum coefficient of static friction μ s between the race car's tires and the track?

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.

Which of the following are appropriate acceleration units?

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.