In Problem 1, What ratio m / M gives the least gravitational potential energy for the system?
Ratio which gives least gravitational potential energy is 0.5
To find the ratio, use the formula for gravitational potential energy in which potential energy is proportional to the product of masses and inversely proportional to the distance between the masses.
Potential Energy, (i)
Ratio of m / M which gives minimum potential energy using equation (i):To find minimum potential energy,
Hence, the ratio at which we obtain least potential energy is 0.5
One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite in a circular orbit above Earth’s surface collides with a pellet having mass .
(a) What is the kinetic energy of the pellet in the reference frame of the satellite just before the collision?
b) What is the ratio of this kinetic energy to the kinetic energy of a bullet from a modern army rifle with a muzzle speed of ?
Figure 13-46a shows a particle A that can be movedalong a y-axis from an infinite distance to the origin. That origin liesat the midpoint between particles B and C, which have identical masses, and the y axis is a perpendicular bisector between them.Distance D is . Figure 13-46b shows the potential energyU of the three-particle system as a function of the position of particle A along the y axis. The curve actually extends rightward and approaches an asymptote of as . What are themasses of (a) particles B and C and (b) particle A?
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