Deck 5: Circular Motion

Question 1

If a satellite moves with constant speed in a perfectly circular orbit around the earth,what is the direction of the acceleration of the satellite?

A)in the forward direction
B)in the backward direction
C)outward away from the earth
D)inward toward the earth
E)The acceleration is zero because the speed is constant.

Answer 1

D

Question 2

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If g_m is the free-fall acceleration at the surface of Mars,what is the free-fall acceleration at the location of the satellite?

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

Answer 2

E

Question 3

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,the gravitational force that the planet exerts on you would be

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

Answer 3

A

Question 4

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)moves along a straight-line path in its original direction.
D)continues to follow a circular path, but with a radius larger than the original radius.
E)moves along a path that is neither straight nor circular.

Question 5

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)the normal force exerted on the car by the road perpendicular to the road
B)the friction force exerted by the road on the car
C)the force that Earth exerts on the car
D)No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Question 6

Two small objects,with masses m and M,are originally a distance r apart,and the magnitude of the gravitational force they exert 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)F/16
B)F/4
C)16F
D)4F
E)F/2

Question 7

Two planets have the same free-fall acceleration on the surface,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/
B)m
C)m
D)4m
E)m/4

Question 8

The Moon is accelerated toward the earth,so it is gradually getting closer to the earth.
C)The moon is not accelerated toward the earth.

Question 9

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

Question 10

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 free-fall acceleration on the planet in terms of g,the free-fall acceleration at the surface of the earth?

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

Question 11

Two small balls,A and B,attract each other gravitationally,exerting a force of magnitude F on each other.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force that they exert on each one?

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

Question 12

When a car goes around a banked circular curve at the proper speed for the banking angle,what force cause it to follow the circular path?

A)the normal force exerted by the road on the car perpendicular to the road's surface
B)the friction force exerted by the road on the car
C)the force that Earth exerts on the car
D)No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.

Question 13

An object moves in a circular path at a constant speed.Compare the direction of the object's velocity and acceleration vectors.

A)Both vectors point in the same direction.
B)The vectors point in opposite directions.
C)The vectors are perpendicular to each other.
D)The acceleration is zero but the velocity is constant.

Question 14

A spaceship is traveling to the Moon.At what point is there no more gravitational force exerted on it by Earth?

A)when it gets above the atmosphere
B)when it is half-way there
C)when it is closer to the Moon than it is to Earth
D)There is no point where there is no more gravitational force exerted on the spaceship by Earth

Question 15

Shown below are the velocity and acceleration vectors for an object in several different types of motion.In which case is the object's velocity changing while its speed is not changing?

Question 16

A car goes around a circular curve on a horizontal road at constant speed.What is the direction of the friction force exerted on the car by the road?

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

Question 17

When an object moves in uniform circular motion,the direction of its acceleration is

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

Question 18

The free-fall acceleration 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)1/6
B)1/16
C)1/24
D)1/96
E)1/12

Question 19

Two small objects,with masses m and M,are originally a distance r apart,and the gravitational force that they exert on each other 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)F/32
B)F/16
C)16F
D)32F
E)2F

Question 20

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 Earth on the water.

Question 21

The Moon is 3.84 × 10⁸ m from Earth and takes 27.3 days to complete each orbit.What are the magnitude and direction of the acceleration of the Moon,assuming a circular orbit?

Question 22

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

Question 23

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/R
B)T/R²
C)T²/R³
D)T³/R²
E)T²/R

Question 24

A child sits on a merry-go-round,1.5 meters from the center.The merry-go-round is turning at a constant rate,and the child is observed to have a radial acceleration of 2.3 m/s².How long does it take for the merry-go-round to make one revolution?

Question 25

The reason an astronaut in an Earth satellite feels weightless is that

A)the astronaut is beyond the range of the earth's gravitational pull.
B)the astronaut is in the state of free fall.
C)the astronaut is at a point in space where the effects of the Moon's gravity and Earth's gravity cancel.
D)this is a psychological effect associated with rapid motion.
E)the astronaut's acceleration is zero.

Question 26

A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation.What is the acceleration of that point due to the spin of the wheel?

A)0.050 m/s²
B)1.4 m/s²
C)48 m/s²
D)200 m/s²
E)0.00 m/s²

Question 27

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive.What is the radius of curvature of this section of the dive?

A)1.2 km
B)5.8 km
C)0.64 km
D)9.2 km
E)7.0 km

Question 28

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

Question 29

Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of diameter 60 m.What are the magnitude and direction of her acceleration?

Question 30

A disk-shaped space station 125 m in diameter spins at a uniform rate about an axis through its center and perpendicular to the plane of the disk.If the acceleration of a point on the rim of the disk is to be equal to g,how long does it take for the station to make one revolution? Use g = 9.8 m/s².

Question 31

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

Question 32

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

Question 33

You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning.What should be the diameter of this wheel?

Question 34

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter.What is the magnitude of the acceleration of the car?

A)0 m/s²
B)1.0 m/s²
C)10 m/s²
D)0.63 m/s²
E)2.2 m/s²

Question 35

The maximum acceleration a pilot can stand without blacking out is about 7.0 g.In an endurance test for a jet plane's pilot,what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m?

Question 36

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

Question 37

Planet A has twice the mass of Planet B.From this information,what can we conclude about the free-fall acceleration at the surface of Planet A compared to that at the surface of Planet B?

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

Question 38

An object moves with a constant speed of 30 m/s on a circular track of radius 150 m.What is the acceleration of the object?

A)0 m/s²
B)0.17 m/s²
C)5.0 m/s²
D)6.0 m/s²

Question 39

You are driving at on a freeway curve of radius What is the magnitude of your acceleration?

A)36.0 m/s²
B)1.20 m/s²
C)20.8 m/s²
D)0.833 m/s²

Question 40

Two planets have the same free-fall acceleration on the surface,but planet B has twice the mass of planet A.If planet A has radius r,what is the radius of planet B?

A)r/
B)r
C)r
D)4r
E)2r

Question 41

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 42

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)24 m/s
C)34 m/s
D)35 m/s
E)19 m/s

Question 43

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

Question 44

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

Question 45

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

Question 46

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 (the force that the pilot exerts on the seat)is not to exceed 7.0 times his true weight?

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

Question 47

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 sum of the forces exerted on the motorcycle?

A)719 N
B)2.95 × 10³ N
C)1.31 × 10⁴ N
D)4.31 × 10⁴ N

Question 48

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

Question 49

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 sum of the forces exerted on the ball?

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

Question 50

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 force that the string exerts on the bead if the angle α is measured to be 25°?

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

Question 51

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

Question 52

In order to simulate apparent weightlessness for astronauts in training (when the astronauts do not push on a seat),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)79 m/s
B)310 m/s
C)260 m/s
D)160 m/s
E)510 m/s

Question 53

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 force that the string can exert on an object without breaking is 350 N,what is the maximum speed the toy can have without breaking the string?

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

Question 54

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

Question 55

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 gravitational pull of Earth?

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

Question 56

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 force that the string exerts on the ball.

Question 57

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 (the force that the pilot exerts on the seat)of the 70-kg pilot at that point?

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

Question 58

A 20-g bead is attached to a light 120 cm-long string as shown in the figure.If the angle α is measured to be 18°,what is the speed of the bead?

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

Question 59

A jet plane flying 600 m/s has 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)640 m
B)1200 m
C)7100 m
D)9200 m

Question 60

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

Question 61

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 /
B)2v
C)v
D)v/2

Question 62

What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

A)31°
B)41°
C)51°
D)61°

Question 63

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? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Question 64

A highway curve of radius 80 m is banked at 45°.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)9.4 m/s
B)28 m/s
C)780 m/s
D)The curve cannot be taken safely at any speed.

Question 65

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.(G = 6.67 × 10^-11 N ∙ m²/kg²)

A)5.8 × 10^-8 _N
B)8.5 × 10³ _N
C)1.2 × 10^-7 _N
D)9.8 × 10^-10 _N
E)2.0 × 10^-9 _N

Question 66

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°
B)13.5°
C)33.8°
D)56.2°
E)60.9°

Question 67

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 cm/s².What is the mass of each of them? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Question 68

A highway curve of radius 100 m,banked at an angle of 45°,may be negotiated without friction at a speed of

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

Question 69

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 70

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 exerted on it are the gravitational forces exerted by the other two balls? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)3.7 × 10^-8 m/s²
B)2.5 × 10^-8 m/s²
C)1.9 × 10^-8 m/s²
D)4.2 × 10^-8 m/s²
E)6.4 × 10^-8 m/s²

Question 71

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? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)1.6 × 10¹³ N
B)4.4 × 10¹³ N
C)1.0 × 10¹⁴ N
D)2.0 × 10¹⁴ N
E)4.0 × 10¹⁴ N

Question 72

At their closest approach,Venus and Earth are 4.20 × 10¹⁰ m apart.The mass of Venus is 4.87 × 10²⁴ kg,the mass of Earth is 5.97 × 10²⁴ kg,and G = 6.67 × 10^-11 N ∙ m²/kg².What is the magnitude of the gravitational force exerted by Venus on Earth at that point?

A)1.10 × 10¹⁸ N
B)4.62 × 10²⁸ N
C)5.43 × 10²⁶ N
D)6.30 × 10²⁰ N
E)1.72 × 10¹⁹ N

Question 73

When a spacecraft is launched from the earth toward the sun,at what distance from center of the earth will the gravitational forces exerted on it by the sun and earth cancel? Earth's mass is 5.97 × 10²⁴ kg,the sun's mass is 1.99 × 10³⁰ kg,and the Earth-sun distance is 1.5 × 10¹¹ m.

A)1.3 × 10⁸ m
B)2.6 × 10⁸ m
C)1.3 × 10¹⁰ m
D)2.6 × 10¹⁰ m

Question 74

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 in magnitude? The mass of Earth is 5.97 × 10²⁴ kg,the mass of the Moon is 7.35 × 10²² kg,the center-to-center distance between Earth and the Moon is 3.84 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

A)3.45 × 10⁸ m
B)3.84 × 10⁷ m
C)4.69 × 10⁶ m
D)3.83 × 10⁶ m
E)4.69 × 10⁷ m

Question 75

At a given point above Earth's surface,the free-fall acceleration is equal to What is the altitude of this point above Earth's surface? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m)

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

Question 76

A very dense 1500-kg point object (A)and a dense 1200-kg point object (B)are held in place 1.00 m apart on a frictionless table.A third point object 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 object is suddenly released,find the magnitude and direction (toward A or toward
B)of its initial acceleration. (G = 6.67 × 10^-11 N ∙ m²/kg²)

Question 77

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon),how large is the gravitational force exerted on that person by the Moon? The mass of the Moon is 7.35 × 10²² kg,the distance to the Moon is 3.82 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

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

Question 78

A spaceship with a mass of 2.8 × 10⁶ kg is traveling toward two spherical asteroids,each with a mass of 5.0 × 10¹⁶ kg,that are 40 km apart center-to-center.Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line.What is the sum of the gravitational forces exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10^-11 N ∙ m²/kg²)

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

Question 79

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°
B)34°
C)30°
D)28°
E)26°

Question 80

From what height above the surface of the earth should an object be dropped to initially have an acceleration of 0.54g? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m)

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