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(a) An astronaut whose height h is 1.70 m floats "feet down" in an orbiting space shuttle at a distance r = 6.77 x 10^6 m from the center of Earth. What is the difference between the gravitational acceleration at her feet and that at her head?

(b) If the astronaut is now "feet down" at the same orbital radius r of 6.77 x 10^6 m about a black hole of mass M_h = 1.99 x 10^31 kg (which is 10 times our Sun's mass),
what is now the difference between the gravitational acceleration at her feet and that at her head?
The black hole has a surface (called its event horizon) of radius Rh = 2.95 x 10^4 m. Nothing, not even light, can escape from that surface or anywhere inside it.
Note that the astronaut is (wisely) well outside the surface (at r = 229R_h). ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154890

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In Pole to Pole, an early science fiction story by George Griffith, three explorers attempt to travel by capsule through a naturally formed (and, of course, fictional) tunnel directly from the south pole to the north pole (Fig.14-68).
According to the story, as the capsule approaches Earth's center, the gravitational force on the explorers becomes alarmingly large and then, exactly at the center, it suddenly but only momentarily disappears. Then the capsule travels through the second half of the tunnel, to the north pole.
Check Griffith's description by finding the gravitational force on the capsule of mass m when it reaches a distance r from Earth's center.
Assume that Earth is a sphere of uniform density p (mass per unit volume).

Subject: Physics   |   Topic: Mechanics  |   ID: 154892

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An asteroid, headed directly toward Earth, has a speed of 12 km/s relative to the planet when it is at a distance of 10 Earth radii from Earth's center.
Neglecting the effects of Earth's atmosphere on the asteroid, find the asteroid's speed vf when it reaches Earth's surface. ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154893

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Comet Halley orbits about the Sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun, its perihelion distance R_p , of 8.9 x 10^10 m. Table in textbook shows that this is between the orbits of Mercury and Venus.
(a)What is the comet's farthest distance from the Sun, its aphelion distance R_a ?

(b) What is the eccentricity e of the orbit of comet Halley? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154895

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Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has orbital speed v = 270 km/s, orbital period T = 1.70 days, and approximate mass m, = 6MS, where MS is the Sun's mass, 1.99 x 10^30 kg. Assuming that the visible star and its companion star,. which is dark and unseen, are both in circular orbits (see Fig.), determine the approximate mass m2 of the dark star. ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154897

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A playful astronaut releases a bowling ball, of mass m = 7.20 kg, into circular orbit about Earth at an altitude h of 350 km.
(a) What is the mechanical energy E of the ball in its orbit?
(b) What is the mechanical energy E0 of the ball on the launchpad at Cape Canaveral?
From there to the orbit, what is the change Delta_E in the ball's mechanical energy? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154898

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In Fig.14-73 , a gray particle of mass m1 = 0.67 kg is a distance d = 23 cm from one end of a uniform rod with length L = 3.0 m and mass M = 5.0 kg.
What is the magnitude of the gravitational force F on the particle from the rod? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154900

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Consider a pulsar, a collapsed star of extremely high density, with a mass M equal to that of the Sun (1.98 x 10^30 kg), a radius R of only 12 km, and a rotational period T of 0.041 s.
By what percentage does the free-fall acceleration g differ from the gravita¬tional acceleration a_g at the equator of this spherical star? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154901

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A satellite in circular orbit at an altitude h of 230 km above Earth's surface has a period T of 89 min. Determine Earth's mass from these data. ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154902

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Two small spaceships, each with mass m = 2000 kg, are in the circular Earth orbit of Fig., at an altitude h of 400 km. Igor, the commander of one of the ships, arrives at any fixed point in the orbit 90 s ahead of Janeway, the commander of the other ship.

a) What are the period T0 and the speed v_0 of the ships?
(b) At point P in Fig.14-76, Janeway fires an instantaneous burst in the forward direction, reducing her ship's speed by 1.00%. After this burst, she follows the elliptical orbit shown dashed in the fig¬ure.
What are the kinetic energy and potential energy of her ship immediately after the burst?

(c) In Janeway's new elliptical orbit, what are the total energy E, the semimajor axis a, and the orbital period Т? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 154904

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An sub with a mass of 1800 kg is traveling eastbound at 17 m/s while a compact car with mass of 900 kg is traveling west bound with a speed of 15 m/s the cars collide head-on becoming entangled.

a) Find the speed of the entangled cars after the collision

b) Find the change in velocity of each car

c) Find the change in the kinetic energy of the system consisting of both cars.

Subject: Physics   |   Topic: Mechanics  |   ID: 155308

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The manual start of an airplane engine requires accelerating its propeller to 250 rpm during a 180 degree rotation by hand.
Approximating the propeller by a 10 kg, 1m long rod, what force should be applied to its end to start the engine? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 155311

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Meteor Crashing Into Moon
a) How much works is done by the Moon's gravitational field as a 1000 kg meteor comes in from outer space and crashes into the Moon?
Do you expect the work done to be positive or negative?

b) Given your answer in part a) and the meteor was at rest at infinity and ignoring gravitational effects of other celestial bodies, what was the meteor's velocity upon impact with the Moon?


Subject: Physics   |   Topic: Mechanics  |   ID: 155312

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A particle moves under the action of force F = -k^2 / x^3 .
Show that the time required by the particle to reach the centre of force from distance δ is t = δ^2/k . ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 155313

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A child riding on a swing rises to a height 1.0 m above the lowest point. Another child of equal mass who's speed at the lowest point is twice as great will rise,
to the same height twice as high four times as high to a height that depends on the mass
How many times be as high with the increase in energy

Subject: Physics   |   Topic: Mechanics  |   ID: 155314

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A car is behind a truck going 25 m/s on the highway.
The car's driver looks for an opportunity to pass, guessing that his car can accelerate at 1.0 m/s2 . He gauges that he has to cover the 20 m of the truck plus 10 m clear room at the rear of the truck and 10 m more at the front of it. In the oncoming lane he sees a car approaching, also traveling at 25 m/s. the car is about 400 meters away.
Should he attempt the pass?
Give details.

Subject: Physics   |   Topic: Mechanics  |   ID: 155315

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Two identical pucks , each with a mass of 1.00 kg are on an air table. Puck A has an initial velocity of 5.00 m/s in the positive x direction. Puck B is at rest. Puck A collides with Puck B, Puck A moves off at 1.00 m/s at an angle of 60.00 above the x axis. What is the speed and direction of Puck B after the collision? ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 155350

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At certain altitude H above the surface of the earth, the gravitational field g falls 76% of its

value at sea level.

Find H (use r=R+H)
Find the escape velocity from that point (you must derive the expression for Ve)

Subject: Physics   |   Topic: Mechanics  |   ID: 155351

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a). A block of mass m = 7.00 kg is attached to the end of an ideal spring. Due to the weight of the block, the block remains at rest when the spring is stretched a distance h= 5.00 cm from its equilibrium length. (See figure) The spring has an unknown spring constant k. Take the acceleration due to gravity to be g = 9.81 m/s^2.

What is the spring constant k?
Express your answer in newtons per meter.

b). Suppose that the block gets bumped and undergoes a small vertical displacement. Find the resulting angular frequency  of the block's oscillations about its equilibrium position.

2nd question (Fig. 100b: block and spring)

Find the kinetic energy KE of the block at the moment labeled B.
Express your answer in terms of k and A.

3rd question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 51.0 cm. The explorer finds that the pendulum completes 101 full swing cycles in a time of 145 s.

What is the value of the acceleration of gravity on this planet?
Express your answer in meters per second per second.
Express your answer in radians per second.

Subject: Physics   |   Topic: Mechanics  |   ID: 155439

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In Figure (a), a 4.7 kg dog stands on a 18 kg flatboat at distance D = 6.1 m from the shore. It walks 2.6 m along the boat toward shore and then stops.
Assuming no friction between the boat and the water, find how far the dog is then from the shore.

There is shown 3 variants of the solution ...MORE

Subject: Physics   |   Topic: Mechanics  |   ID: 155445

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