CALC An object moving in the xy-plane is subjected to the force $\vec{F}=(2xy\hat{i}+x^2\hat{j})\text{N}$, where x and y are in m. Is this a conservative force?

Write a realistic problem for which this is the correct equation(s).

$T-\left(1500\text{kg}\right)\left(9.8{\text{m/s}}^2\right)=\left(1500\text{kg}\right)\left(1.0{\text{m/s}}^2\right)$

$P=T\left(2.0\text{m/s}\right)$

A particle moving on the x-axis experiences a force given by F_x = qx², where q is a constant. How much work is done on the particle as it moves from x = 0 to x = d?

Draw a pictorial representation.

$T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))$

$P=T(2.0\,\(\text{m/s}\))$

The gravitational attraction between two objects with masses m_A and m_B, separated by distance 𝓍, is F = Gm_Am_B/𝓍², where G is the gravitational constant. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a 1.5 x 10¹³ kg comet is passing the orbit of Mars, heading straight for the sun at a speed of 3.5 x 10⁴ m/s. What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and G = 6.67 x 10^-11 Nm²/kg².

CALC An object moving in the xy-plane is subjected to the force $\vec{F}=(2xy\hat{i}+x^2\hat{j})\text{N}$, where x and y are in m. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?

(II) Two Earth satellites, A and B, each of mass m = 950 kg, are launched into circular orbits around the Earth’s center. Satellite A orbits at an altitude of 4800 km, and satellite B orbits at an altitude of 12,600 km. What are the kinetic energies of the two satellites?

How is potential energy different from kinetic energy?

Which of the following is NOT an example of an energy transformation?