Over a certain region of space, the electrostatic potential pattern is described by function Ï(x, y,z) = C(x^3â2x^2y + 3xz^2 â 2y^2z)

where constant C=38.36 V/m^3, and x, y and z are the Cartesian coordinates of the points within that region. We are interested in the pattern of the electric field E(x, y,z) that corresponds to the given potential. Find the electric field at point A given by its coordinates (x, y,z)= (8.4,-3,-7.9) cm in terms of its Cartesian components: V/m, Ex= Ey= Ez= V/m, V/m.

Required:
What is the magnitude E of the electric field at point A?

Avery hard rubber ball (m = 0.5 kg) is falling vertically at 4 m/s just before it bounces on the floor. the ball rebounds back at essentially the same speed. if the collision with the floor lasts 0.05 s, what is the average force exerted by the floor on the ball?

Aroll in a paper machine is powered by a separately excited dc machine. operating point 1 (under load): the roll typically operates at 764 rpm and must provide 301 nm of torque to oppose the load of the paper. the armature voltage is 230v for this operating point operating point 2 (no load): when the load is removed the speed of the roll increases to 900 rpm (the field characteristics are unchanged) la ea dev m (a) calculate the maximum torque (units of nm) that the motor can supply with this applied voltage (b) calculate the value of the armature resistance, ra (in ohms) (c) at operating point 1 (loaded condition), the field current, i, and the total input power (armature field), are measured to be to be 10 a and 28,600 w respectively. use this information to calculate the value of the field resistance, rf (in ohms). (d) (d) at operating point 1 (loaded condition), calculate the motor efficiency. express your answer as a percent to at least 2 significant digits. (d) if the field voltage is reduced by 1/2, calculate the new stall torque (in nm) of the motor (f). if the field voltage is reduced by 1/2, calculate the new no-load speed (in rad/sec)

The image shows a pendulum in simple harmonic motion the pendulum starts at a and swing to e