Concept explainers
The three type of forces acting on the sail.
Answer to Problem 74PQ
The gravitational force acting on the sail is
Explanation of Solution
Write the expression for the force of gravitation acting on the sail.
Here,
Write the expression for the drag force on the sail.
Here,
Write the expression for the orbital velocity of the sail.
Here,
Write the value for distance between Earth and sail.
Write the expression for the force exerted by the solar radiations on the sail.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the gravitational force acting on the sail is
Want to see more full solutions like this?
Chapter 34 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- You are working at NASA, in a division that is studying the possibility of rotating small spacecraft using radiation pressure from the Sun. You have built a scale model of a spacecraft as shown in Figure P33.47. The central body is a spherical shell with mass m = 0.500 kg and radius R = 15.0 cm. The thin rod extending from each side of the sphere is of mass mr = 50.0 g and of total length = 1.00 m. At each end of the rod arc circular plates of mass mp = 10.0 g and radius rp = 2.00 cm, with the center of each plate located at the end of the rod. One plate is perfectly reflecting and the other is perfectly absorbing. The initial configuration of this model is that it is at rest, mounted on a vertical axle with very low friction. To begin the simulation, you expose the model to sunlight of intensity Is = 1 000 W/m2, directed perpendicularly to the plates, for a time interval of t = 2.0 min. The sunlight is then removed from the model. Determine the angular velocity with which the model now rotates about the axle. Figure P33.47arrow_forwardFigure P24.13 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 50.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m. Calculate (a) the frequency of the wave and (b) the magnetic field B when the electric field has its maximum value in the negative y direction. (c) Write an expression for B with the correct unit vector, with numerical values for Bmax, k, and , and with its magnitude in the form B=Bmaxcos(kxt) Figure P24.13 Problems 13 and 64.arrow_forwardSomeone plans to float a small, totally absorbing sphere 0.500 m above an isotropic point source of light, so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere’s density is 19.0 g/cm3, and its radius is 2.00 mm. (a) What power would be required of the light source? (b) Even if such a source were made, why would the support of the sphere be unstable?arrow_forward
- (a) What is in V/m the maximum electric field for a completely polarized light has an intensity of 180 W/m2? b)What is in T the maximum magnetic field of that light? c) What will the maximum electric field of the light be in V/m after it passes through a linearly polarizing filter with its axis at an 30.0° angle to the light’s polarization direction? d) What will the intensity of the light be after it passes through a linearly polarizing filter with its axis at an 30.0° angle to the light’s polarization direction? e) What is in J/m3 the average energy density ⟨u|u⟩ of the light after it passes the polarizing filter?arrow_forward(a) The distance to Polaris, the North Star, is approximately6.44 x 1018 m. If Polaris were to burn out today, how manyyears would it take to see it disappear? (b) How long doesit take sunlight to reach Earth? (c) How long does it take amicrowave signal to travel from Earth to the Moon and back?(The distance from Earth to the Moon is 3.84 x 105 km.)arrow_forwardAt the top of Earth’s atmosphere, the time-averaged Poynting vector associated with sunlight has a magnitude of about 1.49 kW/m2. a. What is the maximum value for the electric field of a wave of this intensity? Give your answer in volts per meter. b. What is the maximum value for the magnetic field of a wave of this intensity? Give your answer in teslas. c. What is the total power radiated by the sun? Assume that the Earth is 1.5×10111.5×1011 m from the Sun and that sunlight is composed of electromagnetic plane waves. Give your answer in watts.arrow_forward
- The electric part of an electromagnetic wave is given by E(x, t) = 0.75 sin (0.30x t) V/m in SI units. a. What are the amplitudes Emax and Bmax? b. What are the angular wave number and the wavelength? c. What is the propagation velocity? d. What are the angular frequency, frequency, and period?arrow_forward(a) What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this electromagnetic radiation can ablate (reshape) the cornea is directly proportional to wavelength, how much more accurate can this UV radiation be than the shortest visible wavelength of light?arrow_forwardA possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this solar sail. Suppose a sail of area A = 6.00 105 m2 and mass m =6.00 103 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1 370 W/m2. (a) What force is exerted on the sail? (b) What is the sails acceleration? (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval required for the sail to reach the moon, 3.84 108 m away, starting from rest at the Earth.arrow_forward
- The Poynting vector describes a flow of energy whenever electric and magnetic fields are present. Consider a long cylindrical wire of radius r with a current I in the wire, with resistance R and voltage V. From the expressions for the electric field along the wire and the magnetic field around the wire, obtain the magnitude and direction of the Poynting vector at the surface. Show that it accounts for an energy flow into the wire from the fields around it that accounts for the Ohmic heating of the wire.arrow_forwardA uniform circular disk of mass m = 24.0 g and radius r = 40.0 cm hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference as shown in Figure P34.39a. A beam of electromagnetic radiation with intensity 10.0 MW/m2 is incident on the disk, in a direction perpendicular to its surface. The disk is perfectly absorbing, and the resulting radiation pressure makes the disk rotate. Assuming the radiation is always perpendicular to the surface of the disk, find the angle through which the disk rotates from the vertical as it reaches its new equilibrium position shown in Figure 34.39b. Figure 34.39arrow_forwardConsider an electromagnetic wave traveling in the positive y direction. The magnetic field associated with the wave at some location at some instant points in the negative x direction as shown in Figure OQ24.12. What is the direction of the electric field at this position and at this instant? (a) the positive x direction (b) the positive y direction (c) the positive z direction (d) the negative z direction (e) the negative y direction Figure OQ24.12arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning