Concept explainers
An interstellar spacecraft from an advanced civilization is hovering above Earth, as shown in Fig. 12.35. The ship consists of two pods of mass m separated by a rigid shaft of negligible mass and one Earth radius (RE) long. Find (a) the magnitude and direction of the net gravitational force on the ship and (b) the net torque about the center of mass, (c) Show that the ship's center of gravity is displaced approximately 0.083 RE from its center of mass.
FIGURE 12.35 Problem 59
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Additional Science Textbook Solutions
College Physics (10th Edition)
Life in the Universe (4th Edition)
Conceptual Integrated Science
University Physics (14th Edition)
Sears And Zemansky's University Physics With Modern Physics
Conceptual Physical Science (6th Edition)
- Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P11.50). Show that each star has a period given by T2=42d3G(M+m) Proceed as follows: Apply Newtons second law to each star. Note that the center-of-mass condition requires that Mr2 = mr1, where r1 + r2 = d.arrow_forwardFind the center of gravity: R = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ x²} about the x-axis.arrow_forwardConsider a rod of total length 4 m that is free to pivot above its center. The linear mass density of the rod is given by (x) = 6 x4 (kg/m), where x is the distance from the center of the rod. The rod is in outer space, so you don't have to worry about any gravitational torques. There is a 168 N force that acts perpendicularly to the rod at its right end, and there is a 512 N force that acts halfway between the left end of the rod and its center. This force acts at an angle of 33 degrees to the vertical. This scenario is shown below: Calculate the angular acceleration of the rod, in rad/s?. The answer could be positive or negative.arrow_forward
- A 3.2 kg flagpole extends from a wall at an angle of 25° from the horizontal. Its center of gravity is 1.6 m from the point where the pole is attached to the wall. What is the gravitational torque on the flagpole about the point of attachment?arrow_forwardPlease Asaparrow_forwardI Review | C Express your answer in radians per second. Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 6.0x105 km (comparable to our sun); its final radius is 15 km. W2 = rad/s Submit Previous Answers Request Answer For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Anyone can be a ballerina. X Incorrect; Try Again; 4 attempts remainingarrow_forward
- A person pushing a horizontal, uniformly loaded, 20.35 kg wheelbarrow of length ?L is attempting to get it over a step of height,h=0.370R, where R is the wheel's radius. The center of gravity of the wheelbarrow is in the center of the wheelbarrow. What is the horizontal component Px of the minimum force P→ necessary to push the wheelbarrow over the step? The gravitational acceleration is ?=9.81 m/s2.arrow_forwardA small remote-controlled car with mass 1.60 kg moves at aconstant speed of v = 12.0 m/s in a track formed by a vertical circleinside a hollow metal cylinder that has a radius of 5.00 mWhat is the magnitude of the normal force exerted on the car by thewalls of the cylinder at (a) point A (bottom of the track) and (b) point B(top of the track)?arrow_forwardQuestion 9: A uniform round object of mass M and radius R is placed in a box of mass M and length & and they are connected to a block of mass M via string as shown in Figure 5. The coefficients of the static and kinetic friction forces between the box and the surface of the ground as well as between the round object and the box are given by 4, and µk, respectively (g is the gravitational acceleration, the spring and the pulley are assumed to be massless, there is no friction between them, and the string is inextendible.) The system is released from rest. The round object starts rolling without slipping. The moment of inertia of the round object about its center of mass is I. When does the round object hit the edge of the box? M,R,I M Figure 5 Select one: 2(-2R)(31 + 2MR?) MgR (1 – 2µ) (1/2- R)(21 + 3MR?) MgR (1 – 2µ) (e/2-R)(31 +2MR²) MgR (1 – 2µ) 2(l-2R)(21 + 3M R²) MgR (1 – 2µ) (e – 2R)(21 + 3MR²) MgR (1 – 2µ)arrow_forward
- Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 6.00 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force. (The mass of the Sun is 1.99 1030 kg.)arrow_forwardAnswer the question in full details, thank you very much: A uniform, solid 2.5 kg cylinder can rotate about an axis through its center at O. The forces applied are : F1 =45N, F2 =4.3N, F3 = 5.5N,and F4 = 4.8 N. Also, R1 = 10. cmand R3 = 4.2cm. Find the magnitude (in rad/s^2) and direction (+ denotes counterclockwise and — denotes clockwise) of theangular acceleration of the cylinder.arrow_forwardou have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. It is to be constructed in the shape of a hollow ring of mass 51,500 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 120 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning