A 50 kg pump is to be placed at the midspan of a 2.8-m simply supported steel (E 200 109 N/m2) beam. The beam is of rectangular cross section of width 25 cm. What are the allowable values of the cross-sectional height such that the natural frequency is outside the range of 50 to 75 Hz

Aball tossed vertically upward from the ground next to a building passes the bottom of a window 1.8 s after being tossed and passes the top of the window 0.20 s later. the window is 2.0 m high from top to bottom. what was the ball's initial velocity? the unit vector j^ is directed upward. how far is the bottom of the window from the launch position? how high does the ball rise above the launch position?

Select the three ways that the parallel-plate capacitor differs from a car battery.

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=