Il The gravitational attraction between two objects with massesm₁ and m₂, separated by distance x, is F = Gm₁m₂/x2, where G isthe gravitational constant.a. How much work is done by gravity when the separationchanges from x₁ to x₂? Assume x₂ < x₁.b. If one mass is much greater than the other, the larger massstays essentially at rest while the smaller mass moves towardit. Suppose a 1.5 × 10¹3 kg comet is passing the orbit of Mars,heading straight for the sun at a speed of 3.5 x 10 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 thebook, and G = 6.67 x 10-¹¹ Nm²/kg².

a) Write the expression for the work done. Further, integrate the expression and substitute the…

Il The gravitational attraction between two objects with masses m₁ and m₂, separated by distance x, is F = Gm₁m₂/x², where G is the gravitational constant. a. How much work is done by gravity when the separation changes from x₁ to x₂? Assume x₂

Il The gravitational attraction between two objects with masses m₁ and m₂, separated by distance x, is F = Gm₁m₂/x², where G is the gravitational constant. a. How much work is done by gravity when the separation changes from x₁ to x₂? Assume x₂

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter8: Potential Energy And Conservation Of Energy

Section: Chapter Questions

Problem 23P: A cat’s crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3 m/s. Assume...

See similar textbooks

Similar questions

(a) Sketch a graph of the potential energy function U(x)=kx2/2+Aex2 where k , A, and are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass in moving with this potential energy has a velocity v when its position is x = . Show that the particle does not pass 2+2 through the origin unless Amv2=k22(1e a 2 ) .
(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.
(a) How long will it take an 850-kg car with a useful power output of 40.0 hp (1hp=746W) to reach a speed of 15.0 m/s, neglecting friction? (b) How long will this acceleration take if the car also climbs a 3.00-m-high hill in the process?
Integrated Concepts (a) What force must be supplied by an elevator cable to produce an acceleration of 0.800 m/s2 against a 200-N frictional force, if the mass of the loaded elevator is 1500 kg? (b) How much work is done by the cable in lifting the elevator 20.0 m? (c) What is the final speed of the elevator if it starts from rest? (d) How much work went into thermal energy?
Suppose a car travels 108 km at a speed of 30.0 m/s, and uses 2.0 gal of gasoline. Only 30 of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (The energy content of gasoline is about 140 Mi/gal.) (a) What is the magnitude of the force exerted to keep the car moving at constant speed? (b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s?
(a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child? (b) Is the mass of the child a factor in determining his speed at the bottom of the slide? (c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level? (d) If friction is present, how would the conservation-of-energy equation be modified? (e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 12.0 m.
A horizontal force of 20 N is required to keep a 5.0 kg box traveling at a constant speed up a frictionless incline for a vertical height change of 3.0 m. (a) What Is the work done by gravity dining this change in height? (b) What Is the work done by the normal force? (c) What is the work done by the horizontal farce?
(a) Suppose a constant force acts on an object. The force does not vary with time or with the position or the velocity of the object. Start with the general definition for work done by a force W=ifFdr and show that the force is conservative, (b) As a special case, suppose the force F =(3i + 4j)N acts on a particle that moves from O to in Figure P7.43. Calculate the work done by F on the particle as it moves along each one of the three paths shown in the figure and show that the work done along the three paths identical.
An archer pulls her bowstring back 0.400 m by exerting a force that increases uniformly from zero to 230 N. (a) What is the equivalent spring constant of the bow? (b) How much work does the archer do on the string in drawing the bow?
A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.Oc below the horizontal. (a) What is the work done on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using energy considerations. (e) What is the total work done on the cart?
A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0° below the horizontal. (a) What is the work done on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using energy considerations. (e) What is the total work done on the cart?
A cat’s crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3 m/s. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball’s rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak? (d) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height? (e) What if the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand? (f) What is the maximum height the ball reaches?