On a typical clear day, the atmospheric electric field points downward and has a magnitude of approximately 103 n/c. compare the gravitational and electric forces on a small dust particle of mass 1.5 ✕ 10−15 g that carries a single electron charge.

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.

A2000 kg car is rounding a curve of radius 200 m on a level road. the maximum frictional force the road can exert on the tires of the car is 4000 n. what is the highest speed at which the car can round the curve?

Which magnetic property best describes a magnet’s ability to act at a distance? magnets are dipolar. magnets attract only certain objects. magnets have magnetic fields. magnets can transfer their properties to certain materials.