During a thunderstorm, then underside of a cloud becomes positively charged, which induces a negative charge on the ground underneath it (just like two parallel plates). If the potential difference between the cloud and the ground is 1.20 gigavolts (1 GV = 1 x 109V) and the electric field intensity between them is1.92 x 106 N/C, downward, how far above the ground is the bottom of the cloud?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

Suppose a force of 60 n is required to stretch and hold a spring 0.1 m from its equilibrium position. a. assuming the spring obeys hooke's law, find the spring constant k. b. how much work is required to compress the spring 0.5 m from its equilibrium position? c. how much work is required to stretch the spring 0.6 m from its equilibrium position? d. how much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. kequals 600

In the illustration, which two simple machines are being used to enable the student to reach the door? a. inclined plane and pulley b lever and wheel-and-axle c pulley and lever d wheel-and axle and inclined plane