A dynamics cart with a force sensor attached is placed on a level track. Attached to the force sensor is a string of negligible mass that passes over a pulley. A hanging mass is then attached to the free end of the string and the cart is released from rest. Draw a picture of this situation below and label all of the forces present. You should ignore any friction on the axels of the cart and pulley

After the car has traveled half of the length of the track the string is cut. Sketch the velocity vs. position graph of the cart for the entirety of its motion. Assume that the cart released from rest at the origin and the track is 2.0 m in length.

A248-g piece of copper is dropped into 390 ml of water at 22.6 °c. the final temperature of the water was measured as 39.9 °c. calculate the initial temperature of the piece of copper. assume that all heat transfer occurs between the copper and the water. remember, the density of water is 1.0 g/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.

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)