With the springs removed, release the cart from rest on a level track with a hanging mass of 50 g. determine the cart velocity when passing through the photogate 30 cm down the track from the starting point of the car. use conservation of energy to find the theoretical value of the glider’s velocity. (remember that each mass has kinetic energy when the cart passes through the photogate.) experiment

Adelivery truck leaves a warehouse and travels 2.60 km north. the truck makes a left turn and travels 1.25 km west before making another right turn to travel 1.40 km north to arrive at its destination. what is the magnitude and direction of the truck's displacement from the warehouse?

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.

Use the information presented in the graph to answer the questions. which segments show acceleration? which segment indicates that the object is slowing down? what is the velocity of segment b? what is the acceleration of segment b?