9. Work & Energy

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.

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

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

Finish the solution of the problem.

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

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

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. Is this a conservative force?

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?