Avery light 1.0-m-long rod is allowed to rotate about a point 0.25 m from its left side. using unit-vector notation and cross product, find the torque that results about this point from the following forces (all of which are in the xy plane): (a) f1 = 2.0 n acting downward on the left end of the rod, (b) f2 = 2.0 n acting upward on the center of the rod at an angle θ2 = 60º, and (c) f3 = 2.0 n acting downward on the right end of the rod at an angle θ3 = 45º. (d) if the rod has a uniform mass distribution and total mass of 1.0 kg, find the torque about this same point in the absence of any external forces. (e) finally, consider the net torque that results from the rod’s weight plus a force at the same location and in the same direction as f1. what magnitude should this force be in order to have a net torque of zero?

Arock is dropped from a cliff and reaches the ground in 2.70s. at the same time another rock is thrown horizontally from the same height with initial x velocity of 0.95 m/s. what distance will in x will the second rock cover?

In a steady-flow steam power plant system, two adiabatic high-pressure and low-pressure turbines ane used to generate power. superheated steam enters the high-pressure turbine at 8 mpa and 550°c. the steam expands in the high-pressure turbine to a saturated vapor at 3 mpa. in order to increase the powe generation of the power plant, another steam turbine working in a lower pressure ranges is deployed. the outlet vapor from the first turbine is heated up at a boiler to the temperature of 500 c at the constant pressure of first turbine's outlet (3 mpa). then, the vapor enters the second turbine and produces extra work. the exit conditions of the second turbine are 5o kpa and 90 percent quality. if the total power output of the power plant is 25 mw, determine a) the mass flow rate of the water (kg/s). b) heat transfer rate in the boiler (mw). (30 points) 3 mpa 00 c 8 mpa s0 c high pres turbine low pres boiler turbine 50 kpa 3 mpa 09 saturated vapor t heat engine, shown in the figure, operates between high temperature and low temperature of through a heat 4. a carnot tn and tu respectively. this heat engine receives energy from a heat reservoir at t exchanger where the heat transferred is proportional to the temperature difference as ? = k (z,-7, ). it rejects heat at a given low temperature tl. to design the heat engine for maximum work output, find the high temperature, th, as a function of tes and t. (15 points) qe

Aball is thrown upward. at a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. what is the maximum height h reached by the ball? consider air friction to be negligible. 1. h ≈ 10 m 2. h ≈ 50 m 3. h ≈ 30 m 4. h ≈ 40 m 5. h ≈ 20 m 003 10.0 points which of the two object shown below has the greatest kinetic energy? a m b 1 2 m v 2v 1. kinetic energies are the same. 2. a 3. b 4. unable to determine. 004 10.0 points tim, with mass 74.6 kg, climbs a gymnasium rope a distance of 3.1 m. the acceleration of gravity is 9.8 m/s 2 . how much potential energy does tim gain? answer in units of j. 005 10.0 points a car is moving at 64 miles per hour. the kinetic energy of that car is 5 × 105 j. how much energy does the same car have when it moves at 111 miles per hour? answer in units of j. 006 10.0 points an 102 kg man climbs up a 1 m high flight of stairs. the acceleration of gravity is 9.81 m/s 2 . w