The machine B is belt-driven by the electric motor A that has an efficiency of 85%. When the motor is running at 25 rad/s, the tension in the upper part of the belt is 20 lb greater than in the lower part. Determine the power consumption of the motor in horsepower (hp).

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.

The image shows the positions of a car on a roller coaster track. arrange the cars in order based on their gravitational potential energy. begin with the lowest potential energy and end with the highest.

When you see distant streetlights through smog, they look dimmer and redder than they do normally. but when you see the same streetlights through fog or falling snow, they look dimmer but not redder. use your knowledge of the interstellar medium to discuss the relative sizes of the particles in smog, fog, and snowstorms compared to the wavelength of light.