(0, 3.00) m (-4.00, 0) m m1 F12 F32 0 m2 mg -x Three uniform spheres of masses m₁ = 1.50 kg, m₂ = 4.00 kg, and m3 = 5.00 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. 4.449 Note that the positive direction of x is defined to be to the right. I + 8.343 x Remember that superposition allows us to calculate the forces do to each sphere separately and then add the results together. ĵ) × 10-11 N

(0, 3.00) m (-4.00, 0) m m1 F12 F32 0 m2 mg -x Three uniform spheres of masses m₁ = 1.50 kg, m₂ = 4.00 kg, and m3 = 5.00 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. 4.449 Note that the positive direction of x is defined to be to the right. I + 8.343 x Remember that superposition allows us to calculate the forces do to each sphere separately and then add the results together. ĵ) × 10-11 N

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter10: Motion In A Noninertial Reference Frame

Section: Chapter Questions

Problem 10.20P: Calculate the effective gravitational field vector g at Earths surface at the poles and the equator....

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Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?
Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?
the black holė, assun around it. A [ans: 4.5 × 1039 kg] Figure 5 2. Mars orbits the Sun in a nearly circular orbit of radius 2.28 × 10" m. The mass of Mars is 6.42 × 1023 kg. Mars experiences a gravitational force from the Sun of magnitude 1.63 × 1021 N. Calculate the speed of Mars and the period of revolution for Mars in terms of Earth years. A [ans: 2.41 × 10ª m/s; 1.90 Earth years] 3. Calculate the speed of a satellite i 6774656902-5 MUCCON N) 16 x10 DVANCED D.A.L. EL-531XT OFF OME D/NO CA nd F MODE STAT VAR INS ALPHA SET UP DEL RESET O pNOT sin AND cos OR tan1XOR DRG XNOR sin dR COS tan DRG EX log in. +DEG M. abc dx D'M'S RCL STO (x,y) DATA CD. -re -xy oy WOM a y q ( 8 6 ) ncr nPr XS +HEX C I NI8 + 5 4. 9 A PEN
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun. (b) Is the ratio an upper limit estimate or a lower limit estimate?
Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 7.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. in terms of I hat and j hat. ( î + ĵ )x10−11
a met icle an he $ 4 R ▼ 888 F4 Part A Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find U(y)-U(yo)= Fg. ds. where F₁ = -mg j and ds = dy j. Express your answer in terms of m, g, yo, and yf. View Available Hint(s) IVD ΑΣΦ ? U(yf) - U (yo) = Submit Part B Consider the force exerted by a spring that obeys Hooke's law. Find II(₂) II(-). APR tv 28 % 5 F5 T 6 F6 Y & 7 F7 U * 8 ²² de DII F8 ( 9 A DD F9 0 ) O 3 of 26 Review | Constants F10 P I
I have a question for number 45. I tried something but I am not sure how the gravity would come in and have trouble visualizing it. Would it only be factored for the y-component since it is gravity?
Consider an astronaut Alice space station orbiting the earth at a radius R = 4R⊕ from the center, where R⊕ = 6.4 × 10^6 m is the earth’s radius and M⊕ = 5.972 x 10^24 kg. Assume the orbit is circular. Consider a second astronaut Julie who’s far away outside the earth’s gravitational field and is at rest with respect to the earth. 1. Considering only special relativity, how much time does Alice age if Julie ages 1 year? 2. Considering only gravity (not special relativity), how much time does Alice age if Julie ages 1 year? 3. Now considering both of these effects (gravity and special relativity) , how much time does Alice age if Julie ages 1 year?
M. 00 F. %24 D. %23 HP TrueVision HD Pavi Se th Site w Technical A AN Careers Mail - boss Texas Work MOe Homework A College X C O 8 https://www.webassign.net/web/Student/Assignment-Responses/last?dep3D28680740 不。 CTN LIAL The International Space Station has a mass of 4.19 x 105 kg and orbits at a radius of 6.79 x 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 71.4 kg astronaut living inside the station. HINT (a) the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.) N (b) the space station's gravitational potential energy (in J) (c) the weight (in N) of an 71.4 kg astronaut living inside the station Need Help? Watch It Read It MY NOTES ASK YOUR TEACHER PREVIOUS ANSWERS SERCP11 7.5.P.039. 8. [2/2 Points] DETAILS dp AMIN g ong Pva ladurial A 732006020610 ADVANCED AUD insert Oly f5 114 米 $ ヤ % 6 #3 9. %3D K. pa B. 目

Problem 7. Use Kepler's third law (and the reduced mass) to derive the time it will take two baseballs, initially at rest a meter apart in deep space, to hit each other due to gravitational attraction. The mass of a baseball is 145 grams. Ignore the diameter of the baseballs; i.e. assume they are point particles.
Consider the gravitational acceleration on the surface of the Moon and of Mars. 1. What is the acceleration, in meters per square second, due to gravity on the surface of the Moon? You will need to look up the mass and radius of the Moon. gMoon= 2. What is the acceleration, in meters per square second, due to gravity on the surface of Mars? The mass of Mars is 6.418 × 1023 kg and its radius is 3.38 × 106 m. gMars=