The temperature u in a metal ball is proportional to the square of the distance from the center of the ball. Find the rate of heat flow across a sphere S of radius r with center at the center of the ball. SOLUTION Taking the center of the ball to be the origin, we have u(x, y, z)

How much work would be needed to raise the payload from the surface of the moon (i.e., x = r) to an altitude of 5r miles above the surface of the moon (i.e., x = 6r)?

Arocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = 12.80 m/s32t, where the +y-direction is upward. (a) what is the height of the rocket above the surface of the earth at t = 10.0 s? b) what is the speed of the rocket when it is 325 m above the surface of the earth?

Assume you measured the mass of the cart to be (500 ± 1) g and the mass of the additional mass you put on the cart to be (500 ± 1) g as well. since the scale you are using in the lab cannot measure objects heavier than 600g you will have to sum up individual pieces and propagate the error. so what would be the mass and the standard error of the cart and the mass