Deck 5: Circular Motion and Gravitation

Question 1

A ventilation fan has blades 0.50 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?

A) 1.1 m/s²
B) 2.2 m/s²
C) 0.55 m/s²
D) 3.3 m/s²

Answer 1

2.2 m/s²

Question 2

A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 400 N, then what maximum speed can the mass have if the string is not to break?

A) 370 m/s
B) 27 m/s
C) 19 m/s
D) 29 m/s

Answer 2

27 m/s

Question 3

A car is going around a racetrack at constant speed. The curves around the track have different radii. In which turn is the magnitude of the car's acceleration the greatest?

A) It is the greatest in the turn with the greatest radius.
B) It is the greatest in the turn with the smallest radius.
C) The acceleration is zero everywhere because of the constant speed.
D) More information is needed to determine the answer.

Answer 3

It is the greatest in the turn with the smallest radius.

Question 4

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1200g at a radius arm of 15.0 cm?

A) 40.7 rev/s
B) 44.6 rev/s
C) 81.4 rev/s
D) 151 rev/s

Question 5

A point on the rim of a 0.30-m radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.10 m from the center of the same wheel?

A) 1.0 m/s
B) 1.3 m/s
C) 2.7 m/s
D) 8.0 m/s

Question 6

What centripetal force does an 60-kg passenger experience when seated 12 m from the center of a Ferris wheel that rotates once every 4 $\degree$ seconds?

A) 484 N
B) 180 N
C) 914 N
D) 240 N

Question 7

A point on the rim of a 0.25-m radius fan blade has centripetal acceleration of 0.20 m/s². Find the centripetal acceleration of a point 0.1 m from the center of the same wheel.

A) 0.01 m/s²
B) 0.02 m/s²
C) 0.04 m/s²
D) 0.08 m/s²

Question 8

Calculate the linear speed due to the Earth's rotation for a person at 40° north latitude on the Earth. The radius of the Earth is 6.40 *10⁶ m.

A) 74.0 m/s
B) 356 m/s
C) 465 m/s
D) 73.0 m/s

Question 9

A cylindrical space colony 13 km in diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land, and lakes on the inside surface and air and clouds in the center. All this would be held in place by the rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate at its perimeter to produce a 1-g gravitational field at the walls of the cylinder?

A) 200 m/s
B) 250 m/s
C) 650 m rad/s
D) 800 m rad/s

Question 10

At what speed will a car round a 125 m radius curve, banked at a 45 $\degree$ angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

A) 27 m/s
B) 17 m/s
C) 23 m/s
D) 35 m/s

Question 11

Consider a child who is swinging. As she reaches the lowest point in her swing:

A) the tension in the rope is equal to her weight.
B) the tension in the rope is equal to her mass times her acceleration.
C) her acceleration is downward at 9.8 m/s².
D) none of the above.

Question 12

The cutting cord on a gas-powered weed cutter is 0.20 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?

A) 628 m/s
B) 25 m/s
C) 19 m/s
D) 63 m/s

Question 13

An airplane in a wide sweeping "outside" loop can create 0-g inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 180 m/s to create a condition of "weightlessness" inside the aircraft?

A) 1150 m
B) 1800 m
C) 2300 m
D) 3300 m

Question 14

For a point on a spinning disc in uniform circular motion, which of the following is not constant?

A) its speed
B) its period of motion
C) its centripetal acceleration
D) the magnitude of its acceleration

Question 15

At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 10 m/s? (g = 9.8 m/s²)

A) 28 $\degree$
B) 32 $\degree$
C) 16 $\degree$
D) 11 $\degree$

Question 16

Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:

A) upward.
B) down toward the ground.
C) forward.
D) at that moment the acceleration is zero.

Question 17

A 1500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 14 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

A) 0.18
B) 0.30
C) 0.28
D) 0.38

Question 18

A roller coaster, loaded with passengers, has a mass of 3000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? (g = 9.8 m/s²)

A) 2.3 * 10⁴ N
B) 4.7 * 10⁴ N
C) 7.0 * 10⁴ N
D) 1.0 * 10⁴ N

Question 19

A bucket in an old well is hoisted upward by a rope that winds up on a cylinder having a radius of 0.10 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

A) 3.0 rev/s
B) 1.5 rev/s
C) 0.48 rev/s
D) 0.24 rev/s

Question 20

The distance from the center of a Ferris wheel to a passenger seat is 6.0 m. What centripetal acceleration does a passenger experience when the wheel rotates once every 4 $\pi$ seconds?

A) 16.9 m/s²
B) 9.0 m/s²
C) 3.0 m/s²
D) 1.5 m/s²

Question 21

Two objects are in circular orbits of different radii around the Sun. Which object has the lowest orbital speed?

A) The one closest to the Sun.
B) The one farthest from the Sun.
C) Once in orbit around the Sun, all objects have the same orbital speed regardless of distance from the Sun. It is the greater radius and greater resulting circumference that causes the object farther from the Sun to take longer to complete an orbit.
D) This cannot be found without knowing the relative masses of the objects.

Question 22

In order to train for a high-g environment, an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed. In this situation, in which direction is the net force on the astronaut?

A) The net force is down since gravity cannot be turned off.
B) The net force is horizontal toward the center of the circle.
C) The net force is between horizontal toward the center of the circle and straight up, the angle depending on the speed and the radius involved.
D) The net force is zero since the astronaut is moving at constant speed and thus the force has no direction.

Question 23

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 *10⁶ m. What free fall acceleration will the 0.50 kg object experience when at the surface of Planet X?

A) 48 m/s²
B) 20 m/s²
C) 16 m/s²
D) 40 m/s²

Question 24

The Earth's orbit is closest to the Sun in January and farthest from the Sun in July. When is the Earth moving the slowest in orbit?

A) Neither January nor July since the orbital speed of the Earth is a constant.
B) January
C) July
D) This occurs twice a year, in April and in October.

Question 25

A satellite is in a circular orbit about the Earth at a distance of two Earth radii above the surface. What is the speed of the satellite? (The radius of the Earth is 6.4 *10⁶ m, and G = 6.67 *10^-11 N * m²/kg².)

A) 2800 m/s
B) 4600 m/s
C) 5600 m/s
D) 16,800 m/s

Question 26

Somewhere between the Earth and the Moon is a point where the gravitational attraction of the Earth is canceled by the gravitational pull of the Moon. The mass of the Moon is 1/81 that of the Earth. How far from the center of the Earth is this point?

A) 8/9 the way to the Moon
B) 9/10 the way to the Moon
C) 3/4 the way to the Moon
D) 80/81 the way to the Moon

Question 27

Assume that the reference frame is moving with the person indicated in each of the following situations. In which case is the reference frame noninertial?

A) The person is walking at a constant speed along a straight, horizontal sidewalk.
B) The person is walking at a constant speed along a straight sidewalk that is inclined downward at a slight unchanging angle.
C) The person is riding an elevator upward at constant speed.
D) The person is skydiving and is freefalling not yet having opened her parachute.

Question 28

A wheel is rotated about a horizontal axle at a constant angular rate. Next, it is rotated in the opposite direction with the same angular rate. The acceleration at a point on the top of the wheel in the second case as compared to the acceleration in the first case:

A) is in the same direction.
B) is in the opposite direction.
C) is upward.
D) is tangential to the wheel.

Question 29

Geosynchronous satellites orbit the Earth at a distance of 42,000 km from the Earth's center. Their angular speed at this height is the same as the rotation rate of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 2000-kg satellite at this height? The radius of the Earth is . (Hint: Use that gravity behaves as .)

A) 85 N
B) 333 N
C) 411 N
D) 455 N

Question 30

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 * 10⁶ m. What is the mass of Planet X? (G = 6.67* 10^-11 N * m²/kg²)

A) 13* 10¹⁹ kg
B) 17 * 10²² kg
C) 9.6 * 10²⁴ kg
D) 4.8 * 10²⁴ kg

Question 31

If the mass of Venus is 0.786 times that of Earth, and its radius is 0.950 that of Earth, estimate the gravitational acceleration g at the surface of Venus. (g_earth = 9.80 m/s²)

A) 7.31 m/s²
B) 3.73 m/s²
C) 8.27 m/s²
D) 8.53 m/s²

Question 32

An Earth satellite is orbiting at a distance from the Earth's surface equal to two Earth radii. At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?

A) There is no acceleration since the satellite is in orbit.
B) 1/9
C) 1/4
D) The answer is not given.

Question 33

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 * 10⁶ m. What free fall acceleration will the 0.50 kg object experience when transported to a distance of 2.0 *10⁶ m from the surface of this planet?

A) 90 m/s²
B) 8.9 m/s²
C) 13 m/s²
D) 18 m/s²

Question 34

The Earth is 93 million miles (mi) from the Sun and its period of revolution is 1 year = 3.15 *10⁷ s. What is the acceleration of the Earth in its orbit about the Sun?

A) 18.6 mi/s²
B) 9.3 *10^-3 mi/s²
C) 13.6 *10^-6 mi/s²
D) 3.7 *10^-6 mi/s²

Question 35

At an altitude of 3 times the radius of the Earth, the acceleration due to gravity is

A) g/3.
B) g/9.
C) g/27.
D) not given.

Question 36

The acceleration due to gravity at the surface of Planet X is 10 m/s². What is the acceleration due to gravity at an altitude of 4000 km above the surface of this planet?

A) 10 m/s²
B) 8.0 m/s²
C) 4.4 m/s²
D) More information is needed.

Question 37

An object when orbiting the Earth at a distance of three Earth radii from the center of the Earth has a weight of 2.0 N. What is the object's mass? (g at the surface of the Earth is 9.8 m/s²)

A) 0.10 kg
B) 1.8 kg
C) 0.92 kg
D) 1.0 kg

Question 38

If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?

A) 14 m/s²
B) 12 m/s²
C) 8.1 m/s²
D) 6.8 m/s²

Question 39

A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 60 km above the surface of this moon. If the value of g on Io is 2.0 m/s², estimate the speed with which the liquid sulfur left the volcano.

A) 120 m/s
B) 240 m/s
C) 490 m/s
D) 970 m/s

Question 40

If a planet has 9 times the radius of the Earth, but has the same density as the Earth, what is the gravitational acceleration at the surface of the planet? (g = 9.8 m/s²)

A) 29.4 m/s²
B) 88.2 m/s²
C) 265 m/s²
D) 39.2 m/s²

Question 41

At what location does an artificial Earth satellite in elliptical orbit have its lowest speed?

A) nearest the Earth
B) farthest from the Earth
C) between Earth and Moon
D) between Earth and Sun

Question 42

For any object orbiting the Sun, Kepler's Law may be written T² = kr³. If T is measured in years and r in units of the Earth's distance from the Sun, then k = 1. What, therefore, is the time (in years) for Jupiter to orbit the Sun if its mean radius from the Sun is 5.2 times the Earth's distance from the Sun?

A) 5.2 years
B) 6.0 years
C) 12 years
D) 16 years

Question 43

What is (are) the location(s) of the low tide(s) on Earth caused by the gravitation of the Moon? Give the location(s) relative to the line through the Earth's and Moon's centers, line EM.

A) the point on EM on the Earth's surface nearest to the Moon
B) the point on EM on the Earth's surface farthest from the Moon
C) the points on the Earth's surface perpendicular to EM at the Earth's center
D) the points on EM on the Earth's surface nearest to and farthest from the Moon

Question 44

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 4d?

A) 1 km/s
B) 2 km/s
C) 8 km/s
D) 16 km/s

Question 45

Of the known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has:

A) the greatest centripetal acceleration.
B) the greatest period of revolution.
C) the smallest speed.
D) none of the above properties.

Question 46

An asteroid has a perihelion (the orbit's closest approach to the Sun) of 2.5 AU and a period of revolution of 8.0 y. What is its greatest distance from the Sun (its aphelion)? (Hint: For an elliptical orbit, the effective radius of the orbit is half the sum of the nearest distance to the Sun and the greatest distance from the Sun.)

A) 8.0 AU
B) 6.5 AU
C) 5.5 AU
D) 2.5 AU

Question 47

An observation satellite for mapping purposes is placed in a low Earth orbit. In order to see the whole surface of the Earth, which would be the preferred orbit?

A) an equatorial orbit
B) a polar orbit
C) an orbit inclined 45° to the equator
D) It doesn't matter since the Earth turns completely every 24 hours.

Question 48

When the Earth's and Moon's centers are 59 Earth radii apart, what is the ratio of the lunar gravitational force on a 2-kg mass at the point on the Earth nearest to the Moon to the lunar gravitational force on a 2-kg mass at the point on the Earth farthest from the Moon?

A) 118/59
B) (58/60)²
C) (60/58)²
D) The value is not given.

Question 49

An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?

A) nearest the Earth
B) farthest from the Earth
C) between Earth and Moon
D) between Earth and Sun

Question 50

Two satellites are monitored as they orbit the Earth; satellite X is four times as far from the Earth's center as is satellite Y. From Kepler's third law one may conclude that the period of revolution of X is what factor times that of Y?

A) 1/2
B) 2.0
C) 8.0
D) 22.6

Question 51

According to Kepler's laws, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is it that Kepler's laws indicate is at the other focus of the ellipse?

A) nothing
B) the Earth
C) The comet itself passes through the other focus.
D) The tail of the comet stays at the other focus.

Question 52

When it comes to tides, high and low, what is the usual situation on the ocean's coast?

A) one high tide or one low tide a day
B) one high tide and one low tide a day
C) two high tides and two low tides a day
D) high tides in the day and low at night

Question 53

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?

A) greater when the orbital radius is smaller
B) greater when the orbital radius is larger
C) independent of the orbital radius
D) determined mainly by the satellite's mass

Question 54

A double star system with each star having the mass of the Sun has an orbital period of 1 year. A second double star system, also with each star having the mass of the Sun, has an orbital period of 8 years. If the separation of the stars in the first system is d and the orbits in both cases are circular, what is the separation of the stars in the second system?

A) 0.5d
B) 2d
C) 4d
D) 8d

Question 55

In order for a satellite to be geosynchronous, its orbit must:

A) go over the North and South Poles.
B) be over the equator.
C) be over a single longitude.
D) emit television signals.