ch 5 mp hw

5.07) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 mm . At the very bottom, the normal force on the driver is twice his weight.

33.6 m/s

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Two blocks, of masses m1m1 and m2m2, are connected to each other and to a central post by cords as shown in the figure(Figure 1). They rotate about the post at a frequency ff (revolutions per second) on a frictionless horizontal surface at distances r1r1 and r2r2 from the post. Derive an algebraic expression for the tension in the segment of the cord from the post to the block of mass m1m1. Express your answer in terms of some or all of the variables m1m1, m2m2, ff , r1r1, and r2r2. Derive an algebraic expression for the tension in the segment of the cord from the block of mass m1m1 to the block of mass m2m2. Express your answer in terms of some or all of the variables m1m1, m2m2, ff , r1r1, and r2r2.

FT1FT1 = 4π2f2(m1r1+m2r2)4π2f2(m1r1+m2r2) FT2FT2 = 4π2m2r2f24π2m2r2f2 check wa 10/15

Earth's orbit around the Sun is slightly elliptical. Thus, Earth actually gets closer to the Sun during part of the year. What happens to Earth's orbital speed when it is closer to the Sun? a) Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun. b) Earth's orbital speed is less when it is closer to the Sun than when it is farther from the Sun. c) Earth's orbital speed is the same whether it is closer to the Sun or farther from the Sun.

a) Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun.

5.52) a) Determine the time it takes for a satellite to orbit the Earth in a circular "near-Earth" orbit. A "near-Earth" orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. b)Does your result depend on the mass of the satellite?

a) TT = 5.07×103ss b) no

Two objects attract each other gravitationally. If the mass of each object doubles, how does the gravitational force between them change? a) The gravitational force increases by a factor of 4. b) The gravitational force decreases by a factor of 4. c) The gravitational force increases by a factor of 2. d) The gravitational force decreases by a factor of 2. e) The gravitational force remains unchanged.

a) The gravitational force increases by a factor of 4.

5.09) a) What is the maximum speed with which a 1200-kgkg car can round a turn of radius 95.0 mm on a flat road if the coefficient of static friction between tires and road is 0.60? Express your answer to two significant figures and include the appropriate units. b) Is this result independent of the mass of the car?

a) vv = 24 msms b) yes

5.56) a) If a satellite orbits very near the surface of a planet with period TT, derive an algebraic expression for the density (mass/volume) of the planet. b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 minmin.

a) ρ=mV= (3π)/GT^2 b) ρ = 5.4×10^3kg/m^3

Which of the following statements are true? Check all that apply. a) The path of the planets around the Sun is circular in shape. b) The Sun is located at one of the foci of the planets' elliptical orbits. c) The Sun is located at the center of the of the planets' circular orbits. d) The path of the planets around the Sun is elliptical in shape.

b) The Sun is located at one of the foci of the planets' elliptical orbits. d) The path of the planets around the Sun is elliptical in shape.

An object moves in a circular path at a constant speed. What is the direction of the net force acting on the object? a) The net force points in the same direction as the motion of the object. b) The net force is directed toward the center of the circular path. c) The net force points in the direction opposite to the motion of the object. d) The net force is zero because the object is moving with a constant speed. e) The net force is directed away from the center of the circular path.

b) The net force is directed toward the center of the circular path.

An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors? a) The velocity and acceleration vectors point in the same direction. b) The velocity and acceleration vectors are perpendicular. c) The velocity vector points in a direction tangent to the circular path. The acceleration is zero. d) The velocity vector points toward the center of the circular path. The acceleration is zero. e) The velocity and acceleration vectors point in opposite directions.

b) The velocity and acceleration vectors are perpendicular.

Which of the following statements are true? Check all that apply. a) A satellite's velocity and orbital radius are independent of each other. b) A geosynchronous satellite has a period of approximately 28 days. c) A satellite's motion is independent of its mass. d) The launch speed of a satellite determines the shape of its orbit around Earth.

c) A satellite's motion is independent of its mass. d) The launch speed of a satellite determines the shape of its orbit around Earth.

A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth? a) The acceleration due to gravity is 9g. b) The acceleration due to gravity is g/9. c) The acceleration due to gravity is g/27. d) The acceleration due to gravity is g/3. e) The acceleration due to gravity is g. f) The acceleration due to gravity is 3g

c) The acceleration due to gravity is g/27.

A planet is discovered orbiting around a star in the galaxy Andromeda at the same distance from the star as Earth is from the Sun. If that star has four times the mass of our Sun, how does the orbital period of the planet compare to Earth's orbital period? a) The planet's orbital period will be one-fourth Earth's orbital period. b) The planet's orbital period will be equal to Earth's orbital period. c) The planet's orbital period will be twice Earth's orbital period. d) The planet's orbital period will be one-half Earth's orbital period. e) The planet's orbital period will be four times Earth's orbital period.

d) The planet's orbital period will be one-half Earth's orbital period.

Why does a satellite in a circular orbit travel at a constant speed? a) The gravitational force acting on the satellite is balanced by the centrifugal force acting on the satellite. b) The net force acting on the satellite is zero. c) There is a force acting opposite to the direction of the motion of the satellite. d) There is no component of force acting along the direction of motion of the satellite.

d) There is no component of force acting along the direction of motion of the satellite.

Two planets, planet A and planet B, have the same surface gravity. However, planet B has twice the radius of planet A. How does the mass of planet B compare to the mass of planet A? a) The mass of planet B is equal to the mass of planet A. b) The mass of planet B is twice the mass of planet A. c) The mass of planet B is one-half the mass of planet A. d) The mass of planet B is one-fourth the mass of planet A. e) The mass of planet B is four times the mass of planet A.

e) The mass of planet B is four times the mass of planet A. //If the surface gravity is the same, this means that the attractive force exerted by both planets upon any body on the surface ,is the same. This means that FgA and FgB are equal each other, so, applying the Universal Law of Gravitation to both planets, we can write: FgA = G mMa / ra² = FgB = GmMb/rb² Equating both sides, and simplyfing common terms, we have: Ma/ra² = Mb/(2ra)² Solving for Mb: Mb = Ma . (4ra)² / ra² = 4 Ma

5.13) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire) as shown in the figure(Figure 1). The circle formed by the tube has a diameter of about 1.1 kmkm. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (say 0.90 gg) is to be felt? Express your answer using two significant figures.

ff = 1700rev/drev/d

5.32) A hypothetical planet has a radius 1.5 times that of Earth, but has the same mass.

gplanetgplanet = 4.4 ms2

5.31) Two objects attract each other gravitationally with a force of 3.1×10−10 NN when they are 0.55 mm apart. Their total mass is 4.2 kgkg . Find their individual masses.

m1m1, m2m2 = 3.8,0.4 kgkg

5.50) Two satellites orbit Earth at altitudes of 7500 kmkm and 15,000 kmkm above the Earth's surface. Which satellite is faster, and by what factor? the far satellite is moving 1.2 times faster than the close satellite the far satellite is moving 1.5 times faster than the close satellite the close satellite is moving 1.5 times faster than the far satellite the close satellite is moving 1.2 times faster than the far satellite

the close satellite is moving 1.2 times faster than the far satellite

5.22) If a curve with a radius of 82 mm is properly banked for a car traveling 76 km/hkm/h , what must be the coefficient of static friction for a car not to skid when traveling at 95 km/hkm/h ?

μminμmin = 0.21

5.15) A coin is placed 12.0 cmcm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36.0 rpmrpm (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable? Express your answer using three significant figures.

μsμs = 0.174

5.08) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 150 mm at a speed of 128 km/hkm/h ?

μμ = 0.86