gravitational potential energy function U(r) is shown for a planet with mass M and radius R. a) If a projectile is launched from the surface of the planet with a speed equal to the planets escape speed, how fast is the projectile travelling when it reaches a distance r = ∞ ? b) If a satellite orbiting the planet at an altitude of 2R encounters some friction (i.e. a patch of very thin atmosphere) that decreases its speed, what would you expect to happen to the radius of the satellites orbit, and why would you expect that to happen? (4))

gravitational potential energy function U(r) is shown for a planet with mass M and radius R. a) If a projectile is launched from the surface of the planet with a speed equal to the planets escape speed, how fast is the projectile travelling when it reaches a distance r = ∞ ? b) If a satellite orbiting the planet at an altitude of 2R encounters some friction (i.e. a patch of very thin atmosphere) that decreases its speed, what would you expect to happen to the radius of the satellites orbit, and why would you expect that to happen? (4))

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 52P

See similar textbooks

Similar questions

An electron in a television tube is accelerated uniformly from rest to a speed of 8.4107 m/s over a distance of 2.5 cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?
In an iconic movie scene, Forrest Gump (https://openstaxcollege.org/l/21ForrGumpvid) runs around the country. If he is running at a constant speed of 3 m/s, would it take him more or less energy to run uphill or downhill and why?
A particle of mass 2.0 kg moves under the influence of the force F(x)=(3/x)N. If its speed at x=2.0 m is v=6.0 m/s, what is its speed at x = 7.0 m?
A particle of mass 4.0 kg is constrained to move along the x -axis under a single force F(x)=cx3 , where c=8.0N/m3 . The particle’s speed at A, where xA=1.0m , is 6.0 m/s. What is its speed at B, where xB=2.0m ?
Check Your Understanding What potential energy U(x) can you substitute in Equation 8.13 that will result in motion with constant velocity of 2 m/s for a particle of mass 1 kg and mechanical energy 1 J?
A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point; that is Fr3 , if the distance from P to the position of the particle is r. Let b be the proportionality constant, and write the magnitude of the force as F=br3. Find the potential energy of a particle subjected to this force when the particle is at a distance D from P, assuming the potential energy to be zero when the particle is at P.
A 200-g steel ball is tied to a 2.00m “massless” string and hung from the ceiling to make a pendulum, and then, the ball is brought to a position making a 30 angle with the vertical direction and released from rest. Ignoring the effects of the air resistance, find the speed of the ball when the string (a) is vertically down, (b) makes an angle of 20 with the vertical and (c) makes an angle of 10 with the vertical.
Suppose you throw a ball upward and catch it when it returns at the same height. How much work does the gravitational force do on the ball over its entire trip?
A particle of mass 2.0 kg moves under the influence of the force F(x)=(5x2=7x)N . Suppose a frictional force also acts on the particle. If the particle’s speed when it starts at x=4.0 m is 0.0 m/s and when it arrives at x=4.0 m is 9.0 m/s, how much work is done on it by the frictional force between x=4.0 m and x=4.0 m?
Answer yes or no to each of the following questions. (a) Can an objectEarth system have kinetic energy and not gravitational potential energy? (b) Can it have gravitational potential energy and not kinetic energy? (c) Can it have both types of energy at the same moment? (d) Can it have neither?
“ E=K+Uconstant is a special case of the work energy theorem.” Discuss this statement.
A particle of mass 2.0 kg moves under the influence of the force F(x)=(5x2=7x)N. If its speed at x=4.0 m is v=20.0 m/s, what is its speed at x=4.0m ?