Three tiny charged metal balls are arranged on a straight line. the middle ball is positively charged and the two outside balls are negatively charged. the two outside balls are separated by 20 cm and the middle ball is exactly halfway in between. (hint: draw a picture; in your picture, the distance between the two outermost balls should be 20 cm.) the absolute value of the charge on each ball is the same, 1.93 μcoulombs (the meaning of μ, which is read as "micro", is 10-6). give your answers in newtons.

Atransverse wave is traveling on a string stretched along the horizontal x-axis. the equation for the vertical displacement y of the string is given by y = (1.8 x 10-3)cos[π(13x - 60t)], where all quantities are in si units. what is the maximum speed of a particle of the string

Matt is driving down 7th street. he drives 150 meters in 18 sec. assuming he doesn’t slow down or speed up, what is his speed?

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.