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
Additional Science Textbook Solutions
Human Biology: Concepts and Current Issues (8th Edition)
Concepts of Genetics (12th Edition)
Chemistry: The Central Science (14th Edition)
Human Physiology: An Integrated Approach (8th Edition)
Applications and Investigations in Earth Science (9th Edition)
Genetic Analysis: An Integrated Approach (3rd 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 man in a gym is holding an 8.0-kg kettlebell at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the gravitational force on the kettlebell if his arm is held at 30° below the horizontal?arrow_forwardA 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 person pushing a horizontal, uniformly loaded, 26.90 kg wheelbarrow of length ? is attempting to get it over a step of height ℎ=0.470?, where ? is the wheel's radius. The center of gravity of the wheelbarrow is in the center of the wheelbarrow. What is the horizontal component ??of the minimum force ?⃗ necessary to push the wheelbarrow over the step? The gravitational acceleration is ?=9.81 m/s2.arrow_forward
- A 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_forwardYou are to design a rotating cylindrical axle to lift 800 N buckets of cement from the ground to a rooftop 78.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise. (a) What should the diameter of the axle be in order to raise the buckets at a steady 2.00 cm/s when it is turning at 7.5 rpm? (b) If instead the axle must give the buckets an upward acceleration of 0.400 m/s2, what should the angular acceleration of the axle be?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