Physics Test 4

G34. Of the five masses in orbit around the central mass, the one with the longest period of revolution is

4 (furthest)

O14. An object of mass m, oscillating on the end of a spring with spring constant k has amplitude A. Its maximum speed is:

A √(k/m)

G21. The speed of a comet in an elliptical orbit about the sun: A. decreases while it is receding from the sun B. is constant C. is greatest when farthest from the sun D. varies sinusoidally with time E. equals L/(mr), where L is its angular momentum, m is its mass, and r is its distance from the sun

A. decreases while it is receding from the sun

G41. Two satellites, one in geosynchronous orbit ( T = 24 hrs) and one with a period of 12 hrs, are orbiting Earth. How many times larger than the radius of Earth is the distance between the orbits of the two satellites. (Mass(Earth) = 5.98 × 10 24 kg, G = 6.67 × 10 -11 N·m 2, g = 9.81 m/s 2, radius(Earth) = 6.38 × 10 6 m) A. 0.51 B. 2.0 C. 6.6 D. 5.7 E. none of the above

A. 0.51

G9. An object at the surface of Earth (at a distance R from the center of Earth) weighs 90 N. Its weight at a distance 3 R from the center of Earth is: A. 10 N B. 30 N C. 90 N D. 270 N E. 810 N

A. 10 N

O7. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is: A. 2 Hz B. 10 s C. 0.05 Hz D. 2 s E. 0.50 s

A. 2 Hz

T4. Two children notice that they can make a car vibrate up and down by periodically pushing down on it. They notice that the vibrations have the largest amplitude when they push 8 times in 13 seconds. The mass of the car is 1800 kg. What is the effective spring constant of the car's suspension system? A. 2.69 x 10^4 N/m B. 2.99 x 10^4 N/m C. 1110 N/m D. 4750 N/m E. 2750 N/m

A. 2.69 x 10^4 N/m

G38. Two planets have masses M and m, and the ratio M/ m = 25. The distance between the planets is R. The point P, is between the planets as shown, and the distance between M and P is x. At P the gravitational forces on an object due to M and m are equal in magnitude. The value of x is A. 5R/6 B. 25R/36 C. R/25 D. 6R/5 E. None of these is correct.

A. 5 R/6

G44. The radius R of a stable, circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by A. R = GM/v2 B. R = Gv/mM C. R = GM/mv D. R = GmM/v E. R = Gv/M

A. R = GM/v^2

O9. A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be: A. T B. 1.5 T C. 2T D. T/2 E. 4T

A. T

G42. Taking the zero of potential energy to be at the infinite separation of two masses, consider the energy of a body in circular planetary motion. Which of the following statements is valid? A. The total mechanical energy of the system is constant and negative. B. The total mechanical energy of the system is constant and positive. C. The potential energy of the system is equal to the kinetic energy but opposite in sign. D. The potential energy of the system decreases as the radius of the orbit increases. E. None of these is valid.

A. The total mechanical energy of the system is constant and negative.

G35. Which of the following statements is true? A. There is no point in the universe where gravity is precisely zero. B. It is possible to find a point in the universe where gravity from different astronomical objects cancels so it is precisely zero. C. Gravity can give rise to a repulsive force. D. Gravity is a nonconservative force. E. None of the above is true.

A. There is no point in the universe where gravity is precisely zero.

G29. An artificial satellite of Earth nears the end of its life due to air resistance. While still in orbit: A. it moves faster as the orbit lowers B. it moves slower as the orbit lowers C. it slowly spirals away from Earth D. it moves slower in the same orbit but with a decreasing period E. it moves faster in the same orbit but with an increasing period

A. it moves faster as the orbit lowers

G13. An object is dropped from an altitude of one Earth radius above Earth's surface. If M is the mass of Earth and R is its radius the speed of the object just before it hits Earth is given by:

A. squareroot of (GM/R)

O25. A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by: A. the damping force B. the initial amplitude C. the initial velocity D. the force of gravity E. none of the above

A. the damping force

O10. In simple harmonic motion, the magnitude of the acceleration is greatest when: A. the displacement is maximum B. the speed is between zero and its maximum C. the displacement is zero D. the speed is maximum E. the force is zero

A. the displacement is maximum

G40. Suppose a planet exists that has half the mass of Earth and half its radius. On the surface of that planet, the acceleration due to gravity is A. twice that on Earth. B. the same as that on Earth. C. half that on Earth. D. one-fourth that on Earth. E. none of these.

A. twice that on Earth.

G43. A satellite with a mass m is in a stable circular orbit about a planet with a mass M. The universal gravitational constant is G. The radius of the orbit is R. The ratio of the potential energy of the satellite to its kinetic energy is A. -2R B. -2 C. +2G D. 2G/R E. -2G/R

B. -2

O33. A damped oscillator has a decay time constant τ. After time t = τ has passed, the fraction of the amount of energy remaining is A. 0.25 B. 0.37 C. 0.5 D. 0.67 E. 0.75

B. 0.37

Q5. The acceleration due to gravity at the surface of the Earth is g. How far from the center of the Earth must we go for the acceleration to be (1/4)g? A. (1/4)RE B. 2RE C. 4RE D. (1/2)RE

B. 2RE

O22. A spring vibrates in simple harmonic motion according to the equation x = 15 cos πt where x is in centimeters and t is in seconds. The total number of vibrations this body makes in 10 s is A. 0.5 B. 5 C. π D. 15 E. 10

B. 5

G25. A planet is in circular orbit around the Sun. Its distance from the Sun is four times the average distance of Earth from the Sun. The period of this planet, in Earth years, is: A. 4 B. 8 C. 16 D. 64 E. 2.52

B. 8

G32. Which of the following statements is one of Kepler's three laws of planetary motion? A. Only an odd number of planets can orbit the sun. B. A line joining any planet to the sun sweeps out equal areas in equal times. C. All planets move in elliptical orbits with Earth at one focus. D. F = GMm/R2 E. The period of any planet about the sun is proportional to the planet's distance from the sun.

B. A line joining any planet to the sun sweeps out equal areas in equal times.

G4. Let M denote the mass of Earth and let R denote its radius. The ratio g/ G at Earth's surface is: A. R2/M B. M/R2 C. MR2 D. M/R E. R/M

B. M/R^2

G14. A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is: A. R/4 B. R/3 C. R/2 D. R E. 2R

B. R/3

Q8. The amplitude and phase constant of an oscillator are determined by: A. the angular frequency B. both the initial displacement and velocity C. the period D. the initial displacement alone E. the initial velocity alone

B. both the initial displacement and velocity

G37. A woman whose weight on Earth is 500 N is lifted to a height of two Earth radii above the surface of Earth. Her weight A. decreases to one-fifth of the original amount. B. decreases to one-ninth of the original amount. C. decreases to one-third of the original amount. D. decreases to one-half of the original amount. E. decreases to one-quarter of the original amount.

B. decreases to one-ninth of the original amount.

O19. If the length of a simple pendulum is doubled, its period will: A. halve B. increase by a factor of √2 C. decrease by a factor of √2 D. double E. remain the same

B. increase by a factor of √2

O13. A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is: A. is 0.088 rad/s B. is 33 rad/s C. is 200 rad/s D. is 1140 rad/s E. cannot be computed unless the value of M is given

B. is 33 rad/s

O3. A particle moves back and forth along the x axis from x = - A to x = + A, in simple harmonic motion with period T. At time t = 0 it is at x = + A. When t = 0.75 T: A. it is between x = 0 and x = +A and is traveling toward x = -A B. it is at x = 0 and is traveling toward x = +A C. it is at x = +A and is at rest D. it is at x = 0 and is traveling toward x = -A E. it is between x = 0 and x = -A and is traveling toward x = -A

B. it is at x = 0 and is traveling toward x = + A

O2. In simple harmonic motion, the magnitude of the acceleration is: A. constant B. proportional to the displacement C. inversely proportional to the displacement D. greatest when the velocity is greatest E. never greater than g

B. proportional to the displacement

O23. A block on a spring is subjected to a damping force that is proportional to its velocity and to an applied sinuoidal force. The energy dissipated by damping is supplied by: A. the kinetic of the mass B. the applied force C. the potential energy of the spring D. friction E. gravity

B. the applied force

G2. The magnitude of the acceleration of a planet in orbit around the Sun is proportional to: A. the mass of the planet B. the mass of the Sun C. the distance between the planet and the Sun D. the reciprocal of the distance between the planet and the Sun E. the product of the mass of the planet and the mass of the Sun

B. the mass of the Sun

O26. A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be: A. half the natural frequency of the oscillator B. the same as the natural frequency of the oscillator C. twice the natural frequency of the oscillator D. unrelated to the natural frequency of the oscillator E. determined from the maximum speed desired

B. the same as the natural frequency of the oscillator

O5. A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s 2. The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately A. 97.5 cm B. 12.2 cm C. 6.21 cm D. 4.88 m E. 2.44 m

C. 6.21 cm

G8. The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet? A. 24 N B. 48 N C. 96 N D. 192 N E. 600 N

C. 96 N

O21. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. At one point in its motion its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = xm, the kinetic and potential energies are: A. K = 5J and U = 3J B. K = 5J and U = -3J C. K = 0 and U = 8J D. K = 8J and U = 0 E. K = 0 and U = -8J

C. K = 0 and U = 8J

O16. Let U be the potential energy (with the zero at zero displacement) and K be the kinetic energy of a simple harmonic oscillator. U avg and K avg are the average values over a cycle. Then: A. Kavg > Uavg B. Kavg < Uavg C. Kavg = Uavg D. K = 0 when U = 0 E. K + U = 0

C. Kavg = Uavg

Q2. A small satellite is in elliptical orbit around the Earth as shown. If L denotes its angular momentum and K its kinetic energy then: A. L2 > L1 and K2 > K1 B. L2 < L1 and K2 = K1 C. L2 = L1 and K2 > K1 D. L2 = L1 and K2 = K1 E. L2 > L1 and K2 = K1

C. L2 = L1 and K2 > K1

G16. An astronaut finishes some work on the outside of his satellite, which is in circular orbit around the Earth. He leaves his wrench outside the satellite. The wrench will: A. fall directly down to the Earth B. continue in orbit at reduced speed C. continue in orbit with the satellite D. fly off tangentially into space E. spiral down to the Earth

C. continue in orbit with the satellite

G36. If the mass of a planet is doubled while its radius and the radius of orbit of its moon remain constant, the speed of the moon is A. reduced by a factor of square root of 2 B. reduced by a factor of 2. C. increased by a factor of square root of 2 D. not changed. E. increased by a factor of 2.

C. increased by a factor of square root of 2

G31. If the mass of a satellite is doubled while the radius of its orbit remains constant, the speed of the satellite is A. reduced by a factor of 2. B. reduced by a factor of 8. C. not changed. D. increased by a factor of 2. E. increased by a factor of 8.

C. not changed.

G10. If Earth were to rotate only 100 times per year about its axis: A. airplanes flying west to east would make better time B. we would fly off Earth's surface C. our apparent weight would slightly increase D. Earth's atmosphere would float into outer space E. our apparent weight would slightly decrease

C. our apparent weight would slightly increase

G20. In planetary motion the line from the star to the planet sweeps out equal areas in equal times. This is a direct consequence of: A. the conservation of energy B. the conservation of momentum C. the conservation of angular momentum D. the conservation of mass E. none of the above

C. the conservation of angular momentum

Q1. In planetary motion the line from the sun to the planet sweeps out equal areas in equal times. This is a direct consequence of: A. the conservation of energy B. none of these C. the conservation of angular momentum D. the conservation of linear momentum E. the conservation of mass

C. the conservation of angular momentum

G3. Earth exerts a gravitational force on the Moon, keeping it in its orbit. The reaction to this force, in the sense of Newton's third law, is: A. the centripetal force on the Moon B. the nearly circular orbit of the Moon C. the gravitational force exerted on Earth by the Moon D. the tides due to the Moon E. the apple hitting Newton on the head

C. the gravitational force exerted on Earth by the Moon

G23. Planet 1 and planet 2 are both in circular orbits around the same central star. The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1. This means that: A. the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is less than the speed of planet 2 B. the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is less than the speed of planet 2 C. the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is greater than the speed of planet 2 D. the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is greater than the speed of planet 2 E. the planets have the same speed and the same period

C. the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is greater than the speed of planet 2

Q3. If the mass of a satellite is doubled while the radius of the orbit is unchanged, the speed is A. decreased by a factor of 2 B. decreased by a factor of 4 C. unchanged D. increased by a factor of 2 E. increased by a factor of 4

C. unchanged

G24. For a planet in orbit around a star the perihelion distance is rp and its speed at perihelion is vp. The aphelion distance is ra and its speed at aphelion is va. Which of following is true? A. va = vp B. va/ ra = vp/rp C. va ra = vp rp D. va/ r2a = vp/r2p E. va r2a = vp/r2p

C. va ra = vp rp

O11. In simple harmonic motion, the displacement is maximum when the: A. acceleration is zero B. velocity is maximum C. velocity is zero D. kinetic energy is maximum E. momentum is maximum

C. velocity is zero

Q4. A satellite of a mass m is in a stable circular orbit around a planet with a mass M. The ratio of the potential energy to the kinetic energy is A. - 2R B. - 2G/R C. + 2G D. - 2

D. - 2

Q10. An object attached to one end of a spring makes 20 vibrations in 10 s. Its period is: A. 2 Hz B. 2 s C. 10 s D. 0.5 s E. 0.5 Hz

D. 0.5 s

T1. A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the surface of the Earth. A space engineer wants to transfer the satellite to an orbit that is 1500 km above the surface. The amount of work that must be done to accomplish this is A. - 3.43 GJ B. 66.5 GJ C. 3.43 GJ D. 1.72 GJ E. - 1.72 GJ

D. 1.72 GJ

G6. To measure the mass of a planet with the same radius as Earth, an astronaut drops an object from rest (relative to the planet) from an altitude of one radius above the surface. When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth. In units of Earth masses, the mass of the planet is: A. 2 B. 4 C. 8 D. 16 E. 32

D. 16

O28. A 2.50-kg object is attached to a spring of force constant k = 4.50 kN/m. The spring is stretched 10.0 cm from equilibrium and released. What is the maximum kinetic energy of this system? A. 4.50 J B. 45.0 J C. 2.25 × 105 J D. 22.5 J E. 56.0 J

D. 22.5 J

O17. A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic energy is: A. zero B. 12.5 J C. 25 J D. 37.5 J E. 50 J

D. 37.5 J

G39. The acceleration due to gravity at the surface of Earth is g. The radius of Earth is R E. The distance from the center of Earth to a point where the acceleration due to gravity is g/9 is . RE B. 9RE C. RE/3 D. 3RE E. None of these is correct.

D. 3RE

O15. A 3-kg block, attached to a spring, executes simple harmonic motion according tox = 2cos(50 t) where x is in meters and t is in seconds. The spring constant of the spring is: A. 1 N/m B. 100 N/m C. 150 N/m D. 7500 N/m E. none of these

D. 7500 N/m

G30. A spaceship is returning to Earth with its engine turned off. Consider only the gravitational field of Earth and let M be the mass of Earth, m be the mass of the spaceship, and R be the distance from the center of Earth. In moving from position 1 to position 2 the kinetic energy of the spaceship increases by:

D. GMm(R1-R2/R1R2)

G22. A planet travels in an elliptical orbit about a star as shown. At what pair of points is the speed of the planet the same? A. W and S B. P and T C. P and R D. Q and U E. Vand R

D. Q and U

O20. A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2 f: A. increase its length by length to 4L B. increase its length by length to 2L C. decrease its length by length to L/2 D. decrease its length by length to L/ 4 E. decrease its mass by length to < M/4

D. decrease its length by length to L/ 4

O1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared

D. displacement

O8. Frequency f and angular frequency ω are related by A. f = πω B. f = 2πω C. f = ω/π D. f = ω/2π E. f = 2ω/π

D. f = ω/2π

G18. Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium". The statement is: A. false, because no moving body can be in equilibrium B. true, because the Earth does not fall into or fly away from the sun C. false, because the Earth is rotating on its axis and no rotating body can be in equilibrium D. false, because the Earth has a considerable acceleration E. true, because if it were not in equilibrium then buildings and structures would not be stable

D. false, because the Earth has a considerable acceleration

G19. A planet travels in an elliptical orbit about a star X as shown. The magnitude of the acceleration of the planet is: A. greatest at point Q B. greatest at point S C. greatest at point U D. greatest at point W E. the same at all points

D. greatest at point W

G11. An astronaut in an orbiting space-craft feels "weightless" because she: A. is beyond the range of gravity B. is pulled outwards by centrifugal force C. has no acceleration D. has the same acceleration as the space-craft E. is outside Earth's atmosphere

D. has the same acceleration as the space-craft

G27. Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation. Then, the relationship between K and U: A. is K = U B. is K = -U C. is K = U/2 D. is K = -U/2 E. depends on the radius of the orbit

D. is K = -U/2

G1. In the formula F = Gm 1 m 2/ r 2, the quantity G: A. depends on the local value of g B. is used only when the Earth is one of the two masses C. is greatest at the surface of the Earth D. is a universal constant of nature E. is related to the Sun in the same way that g is related to the Earth

D. is a universal constant of nature

Q7. In simple harmonic motion the magnitude of the acceleration is: A. greatest when the velocity is greatest B. inversely proportional to the displacement C. never greater than g D. proportional to the displacement E. constant

D. proportional to the displacement

Q6. The displacement of a simple harmonic oscillator is maximum when: A. the acceleration is zero B. the kinetic energy is maximum C. the velocity is maximum D. the velocity is zero

D. the velocity is zero

O6. An object attached to one end of a spring makes 20 vibrations in 10s. Its period is: A. 2 Hz B. 10 s C. 0.5 Hz D. 2 s E. 0.50 s

E. 0.50 s

Q9. A block with a mass m = 680 g is attached to a spring with k = 65 N/m. The block is pulled 11 cm from equilibrium, on a frictionless surface, and released from rest. at t = 0. What is the maximum speed of the block? A. 3.4 cm/s B. 11 m/s C. 34 cm/s D. 1.1 cm/s E. 1.1 m/s

E. 1.1 m/s

G12. Neglecting air resistance, a 1.0-kg projectile has an escape velocity of about 11 km/s at the surface of Earth. The corresponding escape velocity for a 2.0 kg projectile is: A. 3.5 km/s B. 5.5 km/s C. 7.1 km/s D. 10 km/s E. 11 km/s

E. 11 km/s

O4. A uniform disk ( I cm = MR 2) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is

E. 2pi square root (3R/2g)

T5. A small stone sits on top of a vertical spring and when it is displaced slightly it oscillates up and down with an angular frequency of 11.8 rad/s. What is the maximum amplitude of the oscillations so that the stone remains in contact with the spring? A. 4.0 cm B. 2.0 cm C. 6.0 cm D. 8.0 cm E. 7.0 cm

E. 7.0 cm

G26. A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy: A. L2 > L1 and K2 > K1 B. L2 > L1 and K2 = K1 C. L2 = L1 and K2 = K1 D. L2 < L1 and K2 = K1 E. L2 = L1 and K2 > K1

E. L2 = L1 and K2 > K1

O29. A clock keeps accurate time when the length of its simple pendulum is L. If the length of the pendulum is increased a small amount, which of the following is true? A. The clock will continue to keep accurate time. B. The answer cannot be determined without knowing the final length of the pendulum. C. The clock will run fast. D. The answer cannot be determined without knowing the percentage increase in the length of the pendulum. E. The clock will run slow.

E. The clock will run slow.

O12. The amplitude and phase constant of an oscillator are determined by: A. the frequency B. the angular frequency C. the initial displacement alone D. the initial velocity alone E. both the initial displacement and velocity

E. both the initial displacement and velocity

O24. An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time: A. its amplitude is a decreasing function of time only if the damping constant is large B. its amplitude is a decreasing function of time C. its amplitude is an increasing function of time D. its amplitude increases over some portions of a cycle and decreases over other portions E. its amplitude is constant

E. its amplitude is constant

G15. An artificial satellite of the Earth releases a bomb. Neglecting air resistance, the bomb will: A. strike Earth under the satellite at the instant of release B. strike Earth under the satellite at the instant of impact C. strike Earth ahead of the satellite at the instant of impact D. strike Earth behind the satellite at the instant of impact E. never strikes Earth

E. never strikes Earth

G5. A rocket ship is coasting toward a planet. Its captain wishes to know the value of g at the surface of the planet. This may be inferred by: A. measuring the apparent weight of one of the crew B. measuring the apparent weight of an object of known mass in the ship C. measuring the diameter of the planet D. measuring the density of the planet E. observing the ship's acceleration and correcting for the distance from the center of the planet

E. observing the ship's acceleration and correcting for the distance from the center of the planet

G7. Suppose you have a pendulum clock which keeps correct time on Earth (acceleration due to gravity = 9.8 m/s 2). Without changing the clock, you take it to the Moon (acceleration due to gravity = 1.6 m/s 2). For every hour interval (on Earth) the Moon clock will record: A. (9.8/1.6) times h B. 1 h C. squareroot of (9.8/1.6) h D. (1.6/9.8) h E. squareroot of (1.6/9.8) h

E. squareroot of (1.6/9.8) h

G28. An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2 R. During this move: A. the gravitational force does negative work, the kinetic energy of the satellite system increases, and the potential energy of the Earth-satellite system decreases B. the gravitational force does positive work, the kinetic energy of the satellite increases, and the potential energy of the Earth-satellite system increases C. the gravitational force does positive work, the kinetic energy of the satellite increases, and the potential energy of the Earth-satellite system decreases D. the gravitational force does positive work, the kinetic energy of the satellite decreases, and the potential energy of the Earth-satellite system increases E. the gravitational force does negative work, the kinetic energy of the satellite decreases, and the potential energy of the Earth-satellite system increases

E. the gravitational force does negative work, the kinetic energy of the satellite decreases, and the potential energy of the Earth-satellite system increases

G17. The elliptical orbit of a planet around the Sun is shown on the diagram. Which of the following statements is true? A. the eccentricity of the orbit is less thatn zero B. the eccentricity of the orbit is greater than 1 C. the sun might be at point C D. the sun might be at point D E. the sun might be at point B

E. the sun might be at point B

T2. A projectile of mass m is fired from the south pole of the Earth with an initial speed of vo which is greater than the escape speed. What is the speed of the projectile when it is very far away from Earth? The mass and the radius of the Earth are ME and RE.

√vo^2 - (2GMe/Re)

G33. Of the satellites shown revolving around Earth, the one with the greatest speed is

3 (closest)

O18. A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is

C. +- A/ √2

G45. Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1R E and Satellite Two at an altitude of 2R E where R E = 6370 km is the radius of Earth. What is the ratio of the potential energy of Satellite One to Satellite Two? A. 1/4 B. 2/3 C. 3/2 D. 2 E. 1/2

C. 3/2

T3. The acceleration due to gravity near the surface of the Earth is g. The radius of the Earth is Re. The distance from the center of the Earth to a point where the acceleration due to gravity is (1/9)g is A. 9RE B. none of these C. 3RE D. RE/9 E. RE/3

C. 3RE

O27. A simple way to test if a device can withstand high "g-force" is to attach the device to a vibrating platform. Suppose a device has to withstand up to 5g's, and the amplitude of the oscillation is 5 cm, the frequency of the vibration should be A. 44.3 Hz B. 31.3 Hz C. 5 Hz D. 981 Hz E. 62.6 Hz

C. 5 Hz