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Chapter 11 Solutions
Physics For Scientists And Engineers
- A narrow uniform rod has length 2a. The linear mass density of the rod of the rod is pl is p, so the mass m of a length Part A A point mass is located a perpendicular distance from the center of the rod. Calculate the magnitude of the force that the rod exerts on the point mass. (Hint: Let the rod be along the y-axis with the center of the rod at the origin, and divide the rod into infinitesimal segments that have length dy and that are located at coordinate y. The mass of the segment is dm = pdy. Write expressions for the I- and y-components of the force on the point mass, and integrate from a to +a to find the components of the total force). Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. ΠΙΑΣΦ ? F= Submit Request Answer Part B 1+nz+ n(n+1) 2! -2² + ·2³ +... (|z| < 1).) What does your result become for a r? (Hint: Use the power series (1+z)" Express your answer in terms of the gravitational constant G and some or all of…arrow_forwardA 0.75 kg mass oscillates according to the equation x(t)=Acos(ωt). Here, A=0.67 m and ω=6.5 rad/s. What is the period, in seconds, of this mass?arrow_forwardOne of your summer lunar space camp activities is to launch a 1130 kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 217 km. What gain AU in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36 × 1022 kg and 1740 km, respectively. AU = Jarrow_forward
- The star closest to the Sun is called Proxima Centauri. Proxima Centauri has a radius of101,000 km and a mass of 2.45 ×1029 kg. What is the value of g (the free fallacceleration) on the surface of Proxima Centauri?arrow_forwardOne of your summer lunar space camp activities is to launch a 1170 kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 215 km. What gain AU in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36 x 1022 kg and 1740 km, respectively. AU = -3.63 x108 J Incorrectarrow_forwardYou are an alien on an alien planet orbiting the planet's sun in a circular orbit. You want to find the mass of your sun. You determine the center-to-center distance between your planet and sun to be 6.75E+10 meters. The period of motion of your planet (the length of your year) is 1.21E+7 seconds. You know G=6.67*10^−11Nm2kg2 . What is the mass of your sun?arrow_forward
- Scientists design a new particle accelerator in which protons with mass m= 1.7x 10^−27 (kg) follow a circular trajectory given by r =ccos(kt^2)i+ csin(kt^2)j where c= 5.0 (m) and k= 8.0 x10^4 (radius/s^2) are constants and t is the elapsed time. a) what is the radius of the circle? b) what is the proton’s speed at t = 3.0 s? c) what is the force on the proton at t = 3.0 s? Give your answer in component form.arrow_forwardTwo planets of equal mass orbit a much more massive star. Planet m 1 moves in a circular orbit of radius r 1 = 10^11 m with a period of 2 years (= 6.3 x 10^7 s). Planet m 2 moves in an elliptical orbit with its closes t distance r 1 and its farthest distance r 2 = 1.8 x 10^11 m. a. Find the period of m 2’s orbit. b. The elliptical orbit has greater energy. Which planet has the greater potential energy at point P? Justify. c. Which planet has the greater speed at point P? Justify. d. How does the speed of m 2 at point P compare with the speed at point A? Justify.arrow_forward3. A simple pendulum consists of a pendulum bob of mass M at the end of a "mass-less" string of length L. The pendulum bob oscillates back and forth and is moving at speed v when the string is oriented at a constant angle 0 from vertical. Give answers in terms of L, 0, v, M and/or g. This is similar to the vertical circle from the Circular Motion Experiment worksheet except that we are not going in a full circle. a. Draw the free body diagram of forces acting on the pendulum bob. Include a coordinate system on your diagram showing your choice for the +x and +y directions. b. Write out Newton's 2nd law EF = mã for each direction. X: y: c. What is the tangential acceleration of the pendulum bob? d. Determine the tension of the string. e. What is the magnitude of the total acceleration of the pendulum bob?arrow_forward
- After a long space trip where you are in stasis, your autonomous ship lands you on a planet you don’t recognize. Having the equipment on board the ship to make a pendulum, you put one together with a bob of mass 25 g and a length of 50 cm. You find the period to be 1.4 s. Are you on earth? If not, is the planet you are on more or less massive than earth?arrow_forwardA number of gas giant planets orbiting other stars at distances less than 1 A.U. have been discovered. Because of their proximity to their parent stars, and their compositional similarity to Jupiter, they have been labeled “Hot Jupiters”. The orbital radius of one of these planets is 0.06 A.U. with average orbital speed 600 km/sec. What is the length of this planet’s year in Earth (solar) days? Estimate the mass, M, of its parent star in terms of the mass of the sun (M) using Newton’s first form of Kepler’s 3rd Law. Calculate the star’s luminosity, L, in terms of the luminosity of the sun (L☉), Note: (LL=MM4where L ~ 4 × 1026 W ). The radius of this planet is 1.5 times the radius of Jupiter. Assuming its equilibrium temperature is the temperature at which the planet radiates as much energy as it receives from its star, estimate the temperature of the planet. The value of the planet’s albedo is 0.8. (NOTE: The intensity of the star’s radiant power at a distance d from the star is…arrow_forwardA “semi-infinite” uniform rod occupies the nonnegative x-axis. The rod has a linear density δ, which means that a segment of length dx has a mass of δ dx. A particle of mass M is located at the point (−a, 0). The gravitational force F that the rod exerts on the mass is given by where G is the gravitational constant. Find F.arrow_forward
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