A package of mass 5 kg sits at the equator of an airless asteroid of mass 3.0 x 1020 kg and radius 6.3 x 105 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 237 m/s. We have a large and powerful spring whose stiffness is 1.8 x 105 N/m. How much must we compress the spring? |compression| (a positive number) = m

A package of mass 5 kg sits at the equator of an airless asteroid of mass 3.0 x 1020 kg and radius 6.3 x 105 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 237 m/s. We have a large and powerful spring whose stiffness is 1.8 x 105 N/m. How much must we compress the spring? |compression| (a positive number) = m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Three dimensions. Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass ma. Particle B, at xyz coordinates (3.00d, 1.00d, 3.00d), has mass 4.00ma, and particle C, at coordinates (-2.00d, 1.00d, -1.00d), has mass 2.00ma. A fourth particle D, with mass 3.00ma, is to be placed near the other particles. If distance d = 4.50 m, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on A from B, C, and D is zero? (a) Number Units (b) Number |Units (c) Number Units
13.39 • CALC Consider the ring- shaped object in Fig. E13.39 D. A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane. (a) Calculate the gravitational potential energy U of this system. Take the potential energy to be zero when the two objects are far apart. (b) Show that your answer to part (a) reduces to the expected result when x is much larger than the radius a of the ring. (c) Use F. = -dU/dx to find the magnitude and direction of the force on the particle (see Section 7.4 9). (d) Show that your answer to part (c) reduces to the expected result when x is much larger than a. (e) What are the values of U and F, when x = 0? Explain why these results make sense. Figure E13.39 т M
11. A freely falling solid body passes two measuring points that are 12 m below each other during a time of 1 s. From what height above the upper measuring point starts the free fall of the body? What is its speed at each of the two measuring points? [height 2.566 m; speeds 7.1 m/s and 16.9 m/s]
A pitcher bestows a power of P = 206 W to a baseball of mass m = 0.095 kg for a period of t = 0.28 s. What is the ball's speed in m/s when it leaves his hand?
An Atwood's machine consists of two masses m₁ and m₂ joined by a light cord which passes over a pulley. Initially, the heavier mass is positioned a distance h above the floor. The masses are released from rest. At what speed are the masses moving when the heavier mass strikes the floor? Here m₁ = 4kg, m₂ = 6kg, and h = 3m. The cord is long enough so that the lighter mass does not reach the pulley. Devices like this are used in the construction of elevators. (3.4 m/s)
To form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.84 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i (b) Number (c) Number (d) Units Units Units #
A spring with spring constant k and equilibrium length zero is attached tothe top of a frictionless hoop of radius R. The spring is stretched and connected to a bead of mass m at the bottom of the hoop. At t = 0 the bead is given an initial speed v0 and the bead moves up the hoop. Find the speed of the bead as a function of position on hoop v(θ).
To form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.62 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same?
A mass m = 0.55 kg is pushed against a spring with spring constant k and held in place with a catch. The spring compresses a distance x = 0.22 m. When the catch is removed, the mass leaves the spring and slides along a frictionless circular loop of radius R = 0.20 m. When the mass reaches the top of the loop, the normal force is equal to three times the weight of the mass. (a) What is the velocity of the mass at point A? (b) What are the magnitude and direction of the net force at point A?
A 50.2 g ball of copper has a net charge of 2.2 pC. What fraction of the copper's electrons have been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)
A 0.20-kg mass is attached to a string and then released from rest, swinging in an arc as a pendulum. At the bottom of it swing, where it is 0.80 m above the floor, the string is cut and the mass becomes a projectile. It stricks the floor 0.56 meters (horizontally) from the point it was cut. From what height was the mass originally released?
Zero, a hypothetical planet, has a mass of 4.6 x 1023 kg, a radius of 3.3 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?