Deck 5: Circular Motion; Gravitation

Question 1

Choose the one alternative that best completes the statement or answers the question.
A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road?

A) perpendicular to the curve outward
B) tangent to the curve in the forward direction
C) tangent to the curve opposite to the direction of the car's motion
D) perpendicular to the curve inward
E) There is no friction on the car because its speed is constant.

Answer 1

perpendicular to the curve inward

Question 2

Choose the one alternative that best completes the statement or answers the question.
When an object moves in uniform circular motion, the direction of its acceleration is

A) in the same direction as its velocity vector.
B) depends on the speed of the object.
C) in the opposite direction of its velocity vector.
D) is directed toward the center of its circular path.
E) is directed away from the center of its circular path.

Answer 2

is directed toward the center of its circular path.

Question 3

Choose the one alternative that best completes the statement or answers the question.
Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

A) The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater.
B) The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B.
C) The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B.
D) The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B.
E) We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets.

Answer 3

We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets.

Question 4

Choose the one alternative that best completes the statement or answers the question.
When a car goes around a banked circular curve at the proper speed speed for the banking angle, what force cause it to follow the circular path?

A) the friction force from the road
B) the normal force from the road
C) gravity
D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Question 5

Choose the one alternative that best completes the statement or answers the question.
A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to
Gravity at the surface of the earth?

A) g/8
B) g/16
C) g
D) g/4
E) g/2

Question 6

Choose the one alternative that best completes the statement or answers the question.
Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely
To slide on the pavement as it goes around the curve?

A) the car with the new tires
B) Neither car will slide.
C) the car with the bald tires
D) It depends on if the pavement is wet or dry.

Question 7

Choose the one alternative that best completes the statement or answers the question.
If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does
not spill out. This happens because an outward force balances the pull of gravity on the water.

Question 8

Choose the one alternative that best completes the statement or answers the question.
If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh

A) two times less than you do on Earth.
B) two times more than you do on Earth.
C) the same as you do on Earth.
D) four times more than you do on Earth.

Question 9

Choose the one alternative that best completes the statement or answers the question.
Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is
Changed to 4r. What is the magnitude of the new gravitational force?

A) 16F
B) 4F
C) F/16
D) F/4
E) F/2

Question 10

Choose the one alternative that best completes the statement or answers the question.
Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B?

A) m/4
B) $\mathrm { m } / \sqrt { 2 }$
C) 4m
D) m
E) $m \sqrt { 2 }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is

A) zero.
B) one-third of its weight on the surface of the earth.
C) the same as on the surface of the earth.
D) one-quarter of its weight on the surface of the earth.
E) one-half of its weight on the surface of the earth.

Question 12

Choose the one alternative that best completes the statement or answers the question.
Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the
Distance is changed to r/4. What is the magnitude of the new gravitational force?

A) 16F
B) 32F
C) F/16
D) F/32
E) 2F

Question 13

Choose the one alternative that best completes the statement or answers the question.
The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of
Planet B?

A) 1/24
B) 1/16
C) 1/6
D) 1/12
E) 1/96

Question 14

Choose the one alternative that best completes the statement or answers the question.
A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

A) when it is closer to the Moon than it is to Earth
B) when it is half-way there
C) when it gets above the atmosphere
D) It is never beyond the pull of Earth's gravity.

Question 15

Choose the one alternative that best completes the statement or answers the question.
You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the
Ice, it

A) moves along a straight-line path away from the center of the circle.
B) moves along a straight-line path toward the center of the circle.
C) continues to follow a circular path, but with a radius larger than the original radius.
D) moves along a path that is neither straight nor circular.
E) moves along a straight-line path in its original direction.

Question 16

Choose the one alternative that best completes the statement or answers the question.
Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?

A) 2r
B) r
C) $r \sqrt { 2 }$
D) 4r
E) $r / \sqrt { 2 }$

Question 17

Choose the one alternative that best completes the statement or answers the question.
A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the
Location of the satellite?

A) gm/9
B) gm
C) 0
D) gm/16
E) gm/3

Question 18

Choose the one alternative that best completes the statement or answers the question.
The reason an astronaut in an earth satellite feels weightless is that

A) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
B) this is a psychological effect associated with rapid motion.
C) the astronaut is falling.
D) the astronaut is beyond the range of the earth's gravity.
E) the astronaut's acceleration is zero.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the
Attractive force on each one?

A) F
B) 16 F
C) F/4
D) 4 F
E) 8 F

Question 20

Choose the one alternative that best completes the statement or answers the question.
When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path?

A) gravity
B) the friction force from the road
C) the normal force from the road
D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Question 21

Choose the one alternative that best completes the statement or answers the question.
Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits?

A) $T ^ { 2 } / R 3$
B) $T ^ { 2 } / R$
C) $T / R 2$
D) $T ^ { 3 } / R ^ { 2 }$
E) T/R

Question 22

Choose the one alternative that best completes the statement or answers the question.
Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions?

A) twice as long as the present year
B) the same as the present year
C) 1/4 as long as the present year
D) four times as long as the present year
E) 1/2 as long as the present year

Question 23

Write the word or phrase that best completes each statement or answers the question.
A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform
rotation. A person who normally weighs 670 N is sitting on one of the benches attached at
the rim of the wheel. What is the apparent weight (the normal force exerted on her by the
bench) of the person as she passes through the highest point of her motion?

Question 24

Choose the one alternative that best completes the statement or answers the question.
A car moving at a steady 10 m/s on a level highway encounters a depression that has a circular cross-section with a radius of 30 m. The car maintains its speed as it drives through the depression.
What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at
The bottom of the depression?

A) 790 N
B) 200 N
C) 590 N
D) 390 N
E) 490 N

Question 25

Choose the one alternative that best completes the statement or answers the question.
In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top
Of a vertical circle with a radius of 2.5 km?

A) 510 m/s
B) 160 m/s
C) 310 m/s
D) 260 m/s
E) 79 m/s

Question 26

Choose the one alternative that best completes the statement or answers the question.
The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the
Maximum safe driving speed for this horizontal curved section of highway?

A) 46 m/s
B) 52 m/s
C) 50 m/s
D) 54 m/s
E) 48 m/s

Question 27

Choose the one alternative that best completes the statement or answers the question.
If Earth had twice its present mass but it orbited at the same distance from the sun as it does now, its orbital period would be

A) 6 months.
B) 2 years.
C) 1 year.
D) 3 years.
E) 4 years.

Question 28

Choose the one alternative that best completes the statement or answers the question.
Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius allowable for the vertical
Circle if the pilot's apparent weight is not to exceed 7.0 times his true weight?

A) 2200 m
B) 1700 m
C) 42 m
D) 230 m
E) 1500 m

Question 29

Choose the one alternative that best completes the statement or answers the question.
A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the
Car traverse the loop so that the rider does not fall out while upside down at the top? Assume the
Rider is not strapped to the car.

A) 10.1 m/s
B) 14.9 m/s
C) 11.4 m/s
D) 12.5 m/s

Question 30

Choose the one alternative that best completes the statement or answers the question.
A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball?

A) 50 N
B) 100 N
C) 0 N
D) 40 N
E) 20 N

Question 31

Choose the one alternative that best completes the statement or answers the question.
Satellite A has twice the mass of satellite B, and moves at the same orbital distance from Earth as satellite B. Compare the speeds of the two satellites.

A) The speed of B is four times the speed of A .
B) The speed of B is one-fourth the speed of A .
C) The speed of B is twice the speed of A .
D) The speed of B is one-half the speed of A .
E) The speed of B is equal to the speed of A .

Question 32

Choose the one alternative that best completes the statement or answers the question.
A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.35. At what
Speed will the car begin to skid sideways?

A) 9.3 m/s
B) 19 m/s
C) 24 m/s
D) 35 m/s
E) 34 m/s

Question 33

Choose the one alternative that best completes the statement or answers the question.
A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding?

A) 3000 N
B) 300 N
C) 900 N
D) 9000 N
E) 9800 N

Question 34

Choose the one alternative that best completes the statement or answers the question.
Halley's Comet is in a highly elliptical orbit around the sun. Therefore the orbital speed of Halley's Comet, while traveling around the sun,

A) increases as it nears the Sun.
B) is zero at two points in the orbit.
C) decreases as it nears the Sun.
D) is constant.

Question 35

Choose the one alternative that best completes the statement or answers the question.
A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying?

A) 9200 m
B) 640 m
C) 1200 m
D) 7100 m

Question 36

Choose the one alternative that best completes the statement or answers the question.
Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight
Of the 70-kg pilot at that point?

A) 1400 N
B) 490 N
C) 690 N
D) 2600 N
E) 3300 N

Question 37

Choose the one alternative that best completes the statement or answers the question.
A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand
Without breaking is 350 N. What is the maximum speed the mass can have without breaking the
String?

A) 13 m/s
B) 26 m/s
C) 700 m/s
D) 19 m/s

Question 38

Choose the one alternative that best completes the statement or answers the question.
A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h. What is the magnitude of the net force on the motorcycle?

A) $2.95 \times 10 ^ { 3 } \mathrm {~N}$
B) $4.31 \times 10 ^ { 4 } \mathrm {~N}$
C) $1.31 \times 10 ^ { 4 } \mathrm {~N}$
D) 719 N

Question 39

Choose the one alternative that best completes the statement or answers the question.
A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal
Force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?

A) 590 N
B) 200 N
C) 390 N
D) 790 N
E) 490 N

Question 40

Choose the one alternative that best completes the statement or answers the question.
One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts
Walk on the inside surface of the space station. How long will it take for each rotation of the
Cylinder if it is to provide "normal" gravity for the astronauts?

A) 39 s
B) 4.4 s
C) 6.2 s
D) 28 s

Question 41

Choose the one alternative that best completes the statement or answers the question.
A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle θ is measured to be 18°, what is the speed of the mass?

A) 2.0 m/s
B) 3.8 m/s
C) 1.3 m/s
D) 1.1 m/s
E) 0.55 m/s

Question 42

Choose the one alternative that best completes the statement or answers the question.
When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the sun's mass is $1.99 \times 10^{30} \mathrm {~kg}$ and the Earth-sun distance is 1.5 x $10 ^ { 11 } \mathrm {~m}$

A) $1.3 \times 10 ^ { 10 } \mathrm {~m}$
B) $2.6 \times 10 ^ { 10 } \mathrm {~m}$
C) $2.6 \times 10 ^ { 8 } \mathrm {~m}$
D) $1.3 \times 10 ^ { 8 } \mathrm {~m}$

Question 43

Choose the one alternative that best completes the statement or answers the question.
A highway curve of radius 80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

A) 28 m/s
B) 780 m/s
C) 9.4 m/s
D) The curve cannot be taken safely at any speed.

Question 44

Choose the one alternative that best completes the statement or answers the question.
What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere. $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $8.5 \times 10 ^ { 3 } \mathrm {~N}$
B) $5.8 \times 10 ^ { - 8 } \mathrm {~N}$
C) $2.0 \times 10 ^ { - 9 } \mathrm {~N}$
D) $1.2 \times 10 ^ { - 7 } \mathrm {~N}$
E) $9.8 \times 10 ^ { - 10 } \mathrm {~N}$

Question 45

Write the word or phrase that best completes each statement or answers the question.
What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Question 46

Write the word or phrase that best completes each statement or answers the question.
A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along the line connecting A and B . When the third mass is suddenly released, find the magnitude and direction (toward A or toward B ) of its initial acceleration. $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Question 47

Choose the one alternative that best completes the statement or answers the question.
$\begin{array} { | c | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \\\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \\\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \\\hline\end{array}$
Mithra is an unknown planet that has two moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $1.6 \times 10 ^ { 13 } \mathrm {~N}$
B) $4.4 \times 10 ^ { 13 } \mathrm {~N}$
C) $2.0 \times 10 ^ { 14 } \mathrm {~N}$
D) $1.0 \times 10 ^ { 14 } \mathrm {~N}$
E) $4.0 \times 10 ^ { 14 } \mathrm {~N}$

Question 48

Choose the one alternative that best completes the statement or answers the question.
Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is v . What is the safe speed on the larger-radius curve?

A) $v / 2$
B) $v \sqrt { 2 }$
C) $v / \sqrt { 2 }$
D) $2 v$

Question 49

Write the word or phrase that best completes each statement or answers the question.
Two identical tiny balls of highly compressed matter are 1.50 m apart. When released in an orbiting space station, they accelerate toward each other at $2.00 \mathrm {~cm} / \mathrm { s } ^ { 2 }$
What is the mass of each of them? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Question 50

Choose the one alternative that best completes the statement or answers the question.
As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how Iarge is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 x $10 ^ { 22 } \mathrm {~kg}$ the distance to the Moon is $3.82 \times 10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } .$

A) 0.00024 N
B) 0.24 N
C) 0.0024 N
D) 0.024 N

Question 51

Write the word or phrase that best completes each statement or answers the question.
A curved portion of highway has a radius of curvature of 65 m. As a highway engineer,
you want to bank this curve at the proper angle for a steady speed of 22 m/s.
(a) What banking angle should you specify for this curve?
(b) At the proper banking angle, what normal force and what friction force does the
highway exert on a 750-kg car going around the curve at the proper speed?

Question 52

Choose the one alternative that best completes the statement or answers the question.
A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second
Unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the
Road surface is the same in both cases?

A) 30 m/s
B) 70 m/s
C) 40 m/s
D) 160 m/s
E) 80 m/s

Question 53

Choose the one alternative that best completes the statement or answers the question.
A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of
Friction?

A) $29.1 ^ { \circ }$
B) $13.5 ^ { \circ }$
C) $33.8 ^ { \circ }$
D) $60.9 ^ { \circ }$
E) $56.2 ^ { \circ }$

Question 54

Choose the one alternative that best completes the statement or answers the question.
A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle θ is
Measured to be 25°?

A) 0.041 N
B) 0.20 N
C) 0.089 N
D) 0.46 N
E) 0.22 N

Question 55

Write the word or phrase that best completes each statement or answers the question.
A small 175-g ball on the end of a light string is revolving uniformly on a frictionless
surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s.
(a) What are the magnitude and direction of the acceleration of the ball?
(b) Find the tension in the string.

Question 56

Choose the one alternative that best completes the statement or answers the question.
In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against
The wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the
Passengers can have so they do not fall if the coefficient of static friction between the passengers
And the wall is 0.25?

A) 4.9 m/s
B) 2.3 m/s
C) 3.0 m/s
D) 8.9 m/s
E) It depends on the mass of the passengers.

Question 57

Choose the one alternative that best completes the statement or answers the question.
What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

A) $51 ^ { \circ }$
B) $61 ^ { \circ }$
C) $31 ^ { \circ }$
D) $41 ^ { \circ }$

Question 58

Choose the one alternative that best completes the statement or answers the question.
The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the
Speedway banked?

A) $32 ^ { \circ }$
B) $26 ^ { \circ }$
C) $34 ^ { \circ }$
D) $28 ^ { \circ }$
E) $30 ^ { \circ }$

Question 59

Choose the one alternative that best completes the statement or answers the question.
A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can
Be reduced or even eliminated. How long should each rotation take for a doughnut-shaped
Hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal
Gravity of Earth?

A) 91 min
B) 1.5 min
C) 0.011 min
D) 8.7 min
E) 4.6 min

Question 60

Choose the one alternative that best completes the statement or answers the question.
A highway curve of radius 100 m, banked at an angle of $45 ^ { \circ }$ may be negotiated without friction at a speed of

A) 44 m/s
B) 31 m/s
C) 22 m/s
D) 67 m/s

Question 61

Choose the one alternative that best completes the statement or answers the question.
In another solar system, a planet has an airless moon Zygo that is $4.0 \times 10 ^ { 5 }$ m in diameter. Experiments reveal that a freely falling object at the surface of Zygo accelerates at $0.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the mass of Zygo? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $4.8 \times 10^{20} \mathrm {~kg}$
B) $4.8 \times 10 ^ { 19 } \mathrm {~kg}$
C) $1.2 \times 10^{20} \mathrm {~kg}$
D) $2.4 \times 10^{20} \mathrm {~kg}$
E) $2.4 \times 10 ^ { 19 } \mathrm {~kg}$

Question 62

Choose the one alternative that best completes the statement or answers the question.
By how many newtons does the weight of a 100-kg person decrease when he goes from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is $6.38 \times 10 ^ { 6 } \mathrm {~m}$

A) 1.5 N
B) 0.60 N
C) 9.8 N
D) 3.6 N
E) 2.6 N

Question 63

Choose the one alternative that best completes the statement or answers the question.
An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point?

A) g
B) g/4
C) g/2
D) zero
E) $g / \sqrt { 2 }$

Question 64

Choose the one alternative that best completes the statement or answers the question.
At a distance of 14,000 km from the center of Planet Z-99, the acceleration due to gravity is 32 $\mathrm { m } / \mathrm { s } ^ { 2 }$ What is the acceleration due to gravity at a point 28,000 km from the center of this planet?

A) $8.0 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $16 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $4.0 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $2.0 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $128 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is

A) g/9 .
B) 3g .
C) g/3 .
D) 6g .
E) 9g .

Question 66

Choose the one alternative that best completes the statement or answers the question.
The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit?

A) 9000 N
B) 61 N
C) 110 N
D) 16,000 N

Question 67

Choose the one alternative that best completes the statement or answers the question.
At their closest approach, Venus and Earth are $4.20 \times 10^{10}$ $10^{24} \mathrm {~kg} ,$ the mass of Earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$ What is the magnitude of the gravitational force exerted by Venus on Earth at that point?

A) $6.30 \times 10 ^ { 20 } \mathrm {~N}$
B) $1.72 \times 10 ^ { 19 } \mathrm {~N}$
C) $4.62 \times 10 ^ { 28 } \mathrm {~N}$
D) $5.43 \times 10 ^ { 26 } \mathrm {~N}$
E) $1.10 \times 10 ^ { 18 } \mathrm {~N}$

Question 68

Choose the one alternative that best completes the statement or answers the question.
$\begin{array} { | c | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \\\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \\\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \\\hline\end{array}$
Mithra is an unknown planet that has two airless moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $0.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $0.10 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $0.30 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $0.15 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $0.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 69

Choose the one alternative that best completes the statement or answers the question.
The mass of Pluto is $1.31 \times 10 ^ { 22 } \mathrm {~kg}$ and its radius is $1.15 \times 10 ^ { 6 } \mathrm {~m}$
What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $0.661 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $0.140 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $9.81 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $1.62 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $3.72 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 70

Choose the one alternative that best completes the statement or answers the question.
A spaceship with a mass of $2.8 \times 10 ^ { 6 } \mathrm {~kg}$ mass of $5.0 \times 10 ^ { 16 } \mathrm {~kg}$ joining the asteroids and is aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 \mathrm{~km} away from that midpoint?
$\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) 16,000 N
B) 6,200 N
C) 18,000 N
D) 8,000 N
E) 12,000 N

Question 71

Choose the one alternative that best completes the statement or answers the question.
The mass of the Moon is $7.4 \times 10 ^ { 22 } \mathrm {~kg}$
its radius is $1.74 \times 10 ^ { 3 } \mathrm {~km}$
and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $2.8 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $4.9 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $1.6 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $0.80 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 72

Choose the one alternative that best completes the statement or answers the question.
The radius of the earth is R . At what distance above the earth's surface will the acceleration of gravity be $4.9 \mathrm {~m} / \mathrm { s } ^ { 2 } ?$

A) 0.50 R
B) 1.00 R
C) 1.41 R
D) 0.41 R
E) 0.25 R

Question 73

Choose the one alternative that best completes the statement or answers the question.
Three identical 50-kg balls are held at the corners of an equilateral triangle, 30 cm on each side. If one of the balls is released, what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $3.7 \times 10 ^ { - 8 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $4.2 \times 10 ^ { - 8 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $6.4 \times 10 ^ { - 8 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $2.5 \times 10 ^ { - 8 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $1.9 \times 10 ^ { - 8 } \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 74

Choose the one alternative that best completes the statement or answers the question.
From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54 g ? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times 10 ^ { 24 } \mathrm {~kg} , R \text { earth } = 6.38 \times \right.$ $10 ^ { 6 } \mathrm {~m} \text { ) }$

A) 2900 km
B) 5400 km
C) 2300 km
D) 1700 km

Question 75

Choose the one alternative that best completes the statement or answers the question.
What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

A) 290 N
B) 1160 N
C) 118 N
D) 580 N
E) 1200 N

Question 76

Choose the one alternative that best completes the statement or answers the question.
What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

A) 580 N
B) 290 N
C) 1160 N
D) 1200 N
E) 2320 N

Question 77

Choose the one alternative that best completes the statement or answers the question.
An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest. She also knows that the radius of Z-49 is 3.39 $\times 10 ^ { 6 } \mathrm {~m}$ From this information, what will she determine for the mass of Z-49? $\left( G = 6.67 \times 10 ^ { - 11 } N \right.$ $\left. m ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $9.95 \times 10 ^ { 23 } \mathrm {~kg}$
B) $6.62 \times 10^{23} \mathrm {~kg}$
C) $4.62 \times 10^{23} \mathrm {~kg}$
D) $8.09 \times 10 ^ { 23 } \mathrm {~kg}$
E) $3.30 \times 10 ^ { 23 } \mathrm {~kg}$

Question 78

Choose the one alternative that best completes the statement or answers the question.
At a given point above Earth's surface, the acceleration due to gravity is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$
the altitude of this point above Earth's surface? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times 10 ^ { 24 } \right.$ $\mathrm { kg } , R _ { \text {earth } } = 6.38 \times 10 ^ { 6 } \mathrm {~m} \text { ) }$

A) 1500 km
B) 770 km
C) 2000 km
D) 2400 km
E) 970 km

Question 79

Choose the one alternative that best completes the statement or answers the question.
An object weighs 432 N on the surface of the earth. The earth has radius R . If the object is raised to a height of 3 R above the earth's surface, what is its weight?

A) 108 N
B) 27.0 N
C) 48.0 N
D) 144 N
E) 305 N

Question 80

Choose the one alternative that best completes the statement or answers the question.
What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the mass of the Moon is $7.35 \times 10 ^ { 22 } \mathrm {~kg}$ the center-to-center distance between Earth and the Moon is 3.84 \times $10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$

A) $3.84 \times 10 ^ { 7 } \mathrm {~m}$
B) $3.83 \times 10 ^ { 6 } \mathrm {~m}$
C) $4.69 \times 10 ^ { 7 } \mathrm {~m}$
D) $4.69 \times 10 ^ { 6 } \mathrm {~m}$
E) $3.45 \times 10 ^ { 8 } \mathrm {~m}$