Thea thin rod of cross section a extends along the x-axis from x = 0 to x = l polarization of the rod is along its length and is given by p z =ax^ 2 +b . a) calculate rho rho v and o 2 at each end. b) show explicitly that the total bound charge vanishes in this case.

1. consider the case in which air fills air shocks on a truck trailer. the pressure in the shocks is 2 mpa. the temperature is 300 k. the diameter of the shock piston is 10 cm and the initial length of the cylindrical cavity containing the compressed air is 40 cm. a. the truck is gradually loaded over a period of a day in a static setting. the temperature is held constant for the atmosphere and thus for the gas shock. calculate the compressibility of the air in the shock for this condition when the truck is initially being loaded. b. if the shocks were loaded in a dynamic setting by driving over bumps, what would be the compressibility? state your assumption. c. what is the initial load on the shock if the shock is in an atmospheric 100 kpa? d. if the shock is compressed using the process described in part a, and the air shock compressed air cavity length decreases to 20 cm, what is the additional load applied to the shock?

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?

The bar of prob. 5/82 is repeated here. the ends of the 0.4-m bar remain in contact with their re- spective support surfaces. end b has a velocity of 0.5 m/s and an acceleration of 0.3 m/s2 in the di- rections shown. determine the angular accelera- tion of the bar and the acceleration of end a.