Wanda exerts a constant tension force of 12 N on an essentially massless string to keep a tennis ball (m = 60 g) attached to the end of the string traveling in uniform circular motion above her head at a constant speed of 9.0 m/s. What is the length of the string between her hand and the tennis ball? You may ignore gravity in this problem (assume the motion of the tennis ball and string happen in a purely horizontal plane). A. 41 m B. 0.24 m C. 3.2 cm D. 0.41 m OD O C OB OA

Wanda exerts a constant tension force of 12 N on an essentially massless string to keep a tennis ball (m = 60 g) attached to the end of the string traveling in uniform circular motion above her head at a constant speed of 9.0 m/s. What is the length of the string between her hand and the tennis ball? You may ignore gravity in this problem (assume the motion of the tennis ball and string happen in a purely horizontal plane). A. 41 m B. 0.24 m C. 3.2 cm D. 0.41 m OD O C OB OA

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 56PQ: Consider the Earth and the Moon as a two-particle system. a. Find an expression for the...

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Consider the Earth and the Moon as a two-particle system. a. Find an expression for the gravitational field g of this two-particle system as a function of the distance r from the center of the Earth. (Do not worry about points inside either the Earth or the Moon.) b. Plot the scalar component of g as a function of distance from the center of the Earth.
Since March 2006, NASAs Mars Reconnaissance Orbiter (MRO) has been in a circular orbit at an altitude of 316 km around Mars (Fig. P6.81). The acceleration due to gravity on the surface of the planet Mars is 0.376g, and its radius is 3.40 103 km. Assume the acceleration due to gravity at the satellite is the same as on the planets surface. a. What is MROs orbital speed? B. What is the period of the spacecrafts orbit? FIGURE P6.81
(a) How far from the center of Earth would the net gravitational force of Earth and the Moon on an object be zero? (b) Setting the magnitudes of the forces equal should result in two answers from the quadratic. Do you understand why there are two positions, but only one where the net force is zero?
(a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars? The mass of Mars is SW 6.4181023kg and its radius is 3.38106m .
(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?
A Suppose a planet with mass m is orbiting star with mass M and the mean distance between the planet and the star is a. Using Newtons law of universal gravity, derive an algebraic expression for the speed of the planet when it is at the mean distance from the star.
Review An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and Part A finds that it takes the rock 0.600 s to fall 1.90 m. If the radius of the planet is 8.60 × 10' m, what is the mass of the planet? Express your answer with the appropriate units. HÅ mp = Value Units Submit Request Answer
▼ Part C Finally, consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and direction of such a force are given by Newton's law of gravity: Gm1m₂ FG F. 72 where ds dr; G, m₁, and m₂ are constants; and r > 0. Find U(rf) – U(ro) = − SFG · ds. Express your answer in terms of G, m₁, m2, ro, and rf. View Available Hint(s) ΫΠ' ΑΣΦ 5 d C ? U(re)-U(ro) = Submit APR 28 MOLA 888 F4 % 5 F5 T G 6 F6 Y H & 7 tv F7 U * 00 8 . DII F8 ZAO F9 9 K 0 A F10 P ( F11
A baseball of mass m = 0.56 kg is spun vertically on a massless string of length L = 0.68 m. The string can only support a tension of Tmax = 10.3 N before it will break. a.) What is the maximum possible speed of the ball at the top of the loop, in meters per second? b.) What is the maximum possible speed of the ball at the bottom of the loop, in meters per second?
A broken spaceship is located 10 km above the center of a large circular thin sheet of unknown dust. The sheet has a radius of 106 km and a density of 71011 kg/m2. The spaceship and the dust attract each other due to the gravitational force. a. Find the initial acceleration of the spaceship. b. Find the acceleration of the spaceship right before the spaceship hits the dust. c. What will the astronauts in the spaceship experience right before the spaceship hits the dust?
A skateboarder is attempting to skate through a vertical loop of radius r = 7.5 m. He skates down a ramp and is launched into the loop by an inclined plane that makes an angle of θ = 45 degrees with respect to the horizontal. a. If the skateboarder begins from rest how high does the ramp he starts from have to be so that he does not fall at the top of the loop? Give your answer in meters.
Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light-years and an orbital speed of about 200 km/s. a. Determine the mass of the object at the center of the Milky Way galaxy. Give your answer both in kilograms and in solar masses (one solar mass is the mass of the sun). b. Observations of stars, as well as theories of the structure of stars, suggest that it is impossible for a single star to have a mass of more than about 50 solar masses. Can this massive object be a single, ordinary star? c. Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what must the Schwarzschild radius of this black hole be? Would a black hole of this size fit inside the earth's orbit around the sun?