An electron (charge -e) moves in a constant electric field e along the r-axis and a constant magnetic field b along the z-axis. the initial velocity vo of the electron is in the xy-plane z =0 (a) write down the equations of motion in cartesian coordinates. (b) solve the equations of motion. (c) by eliminating time from the solution in b) show that the trajectory of the electron could be viewed as a circle of radius whose center drifts in the negative y-direction with a constant speed e/b (d) use your result in (b) to show that the charges with the same charge/mass ratio (i. e. the same w) and with the identical initial position a(0), y(0), z(0) will end up at the same spot in the xy-plane after one period t = 2π/w regardless of their initial velocities in the ry-plane, thereby demonstrating the charge-focusing ability of crossed constant electric and magnetic field (e) assuming 2 (0)=0, y(0)=0,刘0-0, and y(0) 50, use some graphics package to plot the trajectory of the charge from t-0 to t = 2π/w. (you might want to take that y(0)/w =1 and e/(ub) =1.)

Aspring with a mass of 2 kg has a damping constant 14 kg/s. a force of 3.6 n is required to keep the spring stretched 0.3 m beyond its natural length. the spring is stretched 0.6 m beyond its natural length and then released. find the position of the mass at any time t. (assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)

What is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure? (2 points) as air pressure in an area increases, the density of the gas particles in that area decreases. as air pressure in an area increases, the density of the gas particles in that area increases. as air pressure in an area increases, the density of the gas particles in that area remains constant. as air pressure in an area increases, the density of the gas particles in that area increases and decreases in an alternating pattern. 3. which of the following correctly describes a way in which earth's atmosphere interacts with the geosphere? (2 points) it contains gases that living organisms breathe. it contains gases that trap incoming solar radiation. it provides a medium for cycles that provide nutrients to living organisms. it provides a medium for water to move between earth's surface and the air. 4. which of the following is considered a drawback to using wind energy as a source of power? (2 points) wind energy is nonrenewable. wind energy produces large amounts of air pollution. wind turbines can kill birds that fly through the rotors. wind turbines are built too close to major population centers. 5. a meteorologist predicts that the weather in a region will soon change from clear skies to probable thunderstorms. prior to making this prediction, what did the meteorologist most likely observe on a barometer? (2 points) the barometer fell slightly. the barometer fell substantially. the barometer rose slightly. the barometer rose substantially. 6. which of the following do meteorologists not typically use weather balloons to record? (2 points) atmospheric pressure cloud types humidity temperature 7. during which step in the can crush lab did water vapor force air from the can? (2 points) the can was filled nearly to the top with water. the can was placed on the hot stove top burner for several minutes. the can was removed from the hot stove top burner. the can was placed upside-down in the water-filled pan.

Aforce of 9.00 newtons acts at an angle of 19.0 to the horizontal. what is its component in the horizontal direction?