Deck 6: Circular Motion,orbits,and Gravity

Question 1

An astronaut is in equilibrium when he is positioned 140 km from planet X and 581 km from planet Y,along the straight line joining the planets' centers.What is the ratio of the masses X/Y?

A)0.0581
B)17.2
C)0.241
D)4.15

Answer 1

0.0581

Question 2

Calculate the angular speed,in rad/s of a flywheel turning at 520.0 rpm.

A)54.44 rad/s
B)8.656 rad/s
C)40.83 rad/s
D)60.97 rad/s

Answer 2

54.44 rad/s

Question 3

An electrical motor spins at a constant 2857.0 rpm.If the armature radius is 2.685 cm,what is the acceleration of the edge of the rotor?

A)2403 m/s²
B)844.4 m/s²
C)241,100 m/s²
D)84.40 m/s²

Answer 3

2403 m/s²

Question 4

A 23 kg mass is connected to a nail on a frictionless table by a (massless)string of length 1.3 m.If the tension in the string is 51 N while the mass moves in a uniform circle on the table,how long does it take for the mass to make one complete revolution?

A)4.8 s
B)3.8 s
C)4.5 s
D)5.2 s

Question 5

What is the gravitational force acting on a person due to another person standing 2 meters away? Assume each individual has 59 kg mass.

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 6

The figure shows a 3.0 kg ball tied to the end of a 50 cm long string being swung in a circle in a vertical plane at constant speed.The center of the circle is h = 510 cm above the floor.The ball is swung at the minimum speed necessary to make it over the top without the string going slack.If the string is released at the instant the ball is at the top of the loop,how far to the right of the center of the circle does the ball hit the ground?

A)240 cm
B)230 cm
C)210 cm
D)0.0 cm

Question 7

A ball of mass 8.0 kg is suspended by two wires from a horizontal arm,which is attached to a vertical shaft,as shown in the figure.The shaft is in uniform rotation about its axis such that the linear speed of the ball equals 2.3 m/s.The tension in wire 1 is closest to:

A)39 N
B)49 N
C)29 N
D)20 N
E)9.8 N

Question 8

An aerobatic aircraft is to perform a spiral maneuver.If the engine provides a tangential acceleration of 5.41 m/s²,what is the radial acceleration it will experience at the end of a circle 30.8 m in radius,if the speed at the beginning of the stunt was 55.0 m/s?

A)166 m/s²
B)132 m/s²
C)98 m/s²
D)257 m/s²

Question 9

In an amusement park ride,passengers stand inside an 8 m radius cylinder.Initially,the cylinder rotates with its axis oriented along the vertical.After the cylinder has acquired sufficient speed,it tilts into a vertical plane,that is,the axis tilts into the horizontal,as shown in the figure.Suppose that,once the axis has tilted into the horizontal,the ring rotates once every 4.5 s.If a rider's mass is 40 kg,with how much force does the ring push on her at the top of the ride?

A)230 N
B)620 N
C)1000 N
D)390 N

Question 10

Future space stations will create an artificial gravity by rotating.Consider a cylindrical space station of 380 m diameter rotating about its axis.Astronauts walk on the inside surface of the space station.What rotation period will provide "normal" gravity?

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

Question 11

The weight of spaceman Speff,solely due to the gravitational pull of planet X at its surface,is 389 N.If he moves to a distance of 1.86 × 10⁴ km above the planet's surface,his weight changes to 24.31 N.What is the mass of planet X,if Speff's mass is 75 kg?

A)2.96 × 10²⁴ kg
B)2.96 × 10¹⁸ kg
C)2.96 × 10¹⁷ kg
D)1.59 × 10¹⁸ kg

Question 12

At a given point above the surface of Earth,the gravitational acceleration is equal to 7.8 m/s².The altitude of this point,above the surface of Earth,in km,is closest to:

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

Question 13

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

Question 14

What is the magnitude of the force exerted by Earth on the Moon?

A)2.01 × 10²⁰ N
B)7.67 × 10²⁸ N
C)2.01 × 10²⁶ N
D)7.67 × 10³¹ N

Question 15

A tetherball is on a 2.1 m string that makes an angle of 44° with the vertical as it moves around the pole in a horizontal plane.If the mass of the ball is 1.3 kg,what is the ball's speed?

A)3.7 m/s
B)2.9 m/s
C)3.4 m/s
D)4.2 m/s

Question 16

A satellite is in orbit around a planet.The orbital radius is 34.0 km and the gravitational acceleration at that height is 2.3 m/s².What is the satellite's orbital speed?

A)280 m/s
B)8.8 m/s
C)28 m/s
D)88 m/s

Question 17

Through what angle in degrees does a 33 rpm record turn in 0.25 s?

A)50°
B)28°
C)36°
D)58°

Question 18

The figure shows two wires tied to a 3.3 kg sphere that revolves in a horizontal circle at constant speed.At this particular speed the tension is the same in both wires.What is the tension?

A)24 N
B)32 N
C)44 N
D)22 N

Question 19

The figure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 7.5 m/s.What is the tension in the upper wire?

A)34 N
B)20 N
C)27 N
D)41 N

Question 20

A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor.The tension in the string when the bead is at the very bottom of the circle is 2.2 N.A very sharp knife is suddenly inserted,as shown in the figure,to cut the string directly below the point of support.How far to the right of the center of the circle does the ball hit the floor?

A)160 cm
B)200 cm
C)240 cm
D)190 cm

Question 21

Earth's gravity is caused by our planet's spin on its axis.

Question 22

From what height off the surface of Earth should an object be dropped to initially experience an acceleration of 0.5400 g?

A)2298 km
B)1689 km
C)5426 km
D)2930 km

Question 23

If a highway curve is properly banked and posted at 45 mph,it is a good idea to drive somewhat below this speed if your tires are bald or if the road is icy.

Question 24

Astronauts in orbiting satellites are weightless because they are so far from Earth that its gravitational pull is too weak to feel.

Question 25

Orbiting satellites accelerate toward Earth at 9.8 m/s².

Question 26

Find the orbital speed of an ice cube in the rings of Saturn,if the mass of Saturn is 5.67 x 10²⁶ kg and the rings have an average radius of 100,000 km.

A)19.5 km/s
B)27.5 km/s
C)13.8 km/s
D)1.95 km/s

Question 27

If you swing a bucket of water fast enough in a vertical circle,at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.

Question 28

If you swing a ball in a vertical circle using a thin string,at the bottom of the circle the tension in the string must be greater than the ball's weight.

Question 29

If we assume that an electron is orbiting a proton just like the moon orbits Earth,find the electron's orbital speed due to the gravitational attraction between itself and the proton.Take the orbital radius as 1.00 × 10^-10 m.(This is a very wrong assumption to make. )

A)3.33 × 10^-14 m/s
B)1.11 × 10^-13 m/s
C)1.11 × 10^-27 m/s
D)1.06 × 10^-27 m/s

Question 30

Satellites in orbit are accelerated toward Earth,so they must be getting closer and closer to our planet.

Question 31

Satellites in circular orbits around Earth are in equilibrium because they have uniform speed.

Question 32

An Earth satellite needs to have its orbit changed so the new orbit will be twice as far from the center of Earth as the original orbit.The new orbital period will be twice as long as the original period.

Question 33

You are the science officer on a visit to a distant solar system.Prior to landing on a planet you measure its diameter to be 1.8 × 10⁷ m.You have previously determined that the planet orbits 2.9 × 10¹¹ m from its star with a period of 402 Earth days.Once on the surface you find that the acceleration due to gravity is 19.5 m/s².What are the masses of (a)the planet and (b)the star?

A)(a)2.4 kg × 10²⁵ kg (b)1.2 kg × 10³¹ kg
B)(a)4.3 kg × 10²⁵ kg (b)1.2 kg × 10³¹ kg
C)(a)2.4 kg × 10²⁵ kg (b)7.1 kg × 10³⁰ kg
D)(a)4.3 kg × 10²⁵ kg (b)7.1 kg × 10³⁰ kg

Question 34

While a Ferris wheel turns at uniform angular speed,a seat at the rim of the wheel has a nonzero radial acceleration toward the center of the wheel but a tangential acceleration of zero.

Question 35

An ordinary car would not be able to go around an unbanked curve of a perfectly smooth road,no matter how the driver turned the wheels.

Question 36

A satellite is orbiting Earth.If a payload of material is added until it doubles the satellite's mass,Earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

Question 37

Spaceman Speff orbits planet X with his spaceship.To remain in orbit at 421 km from the planet's center,he should maintain a speed of 80 m/s.What is the mass of planet X?

A)4.0 × 10¹⁹ kg
B)5.1 × 10¹⁷ kg
C)4.0 × 10¹⁶ kg
D)5.1 × 10¹⁴ kg

Question 38

Suppose we want a satellite to revolve around Earth 5 times a day.What should the radius of its orbit be? (Neglect the presence of the Moon. )

A)1.44 × 10⁷ m
B)0.69 × 10⁷ m
C)7.22 × 10⁷ m
D)2.11 × 10⁷ m

Question 39

In the table,the mass of Ekapluto is closest to:

A)1 × 10²² kg
B)3 × 10²² kg
C)1 × 10²³ kg
D)3 × 10²³ kg
E)1 × 10²⁴ kg

Question 40

A proton moving at 0.999 of the speed of light orbits a black hole 4972 km from the center of the attractor.What is the mass of the black hole?

A)6.71 × 10³³ kg
B)6.71 × 10³⁰ kg
C)6.71 × 10³⁶ kg
D)6.71 × 10²⁵ kg

Question 41

A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down.She whirls the rock at the minimum speed (constant in time)such that the string is always taut (no sag).When is the tension the highest?

A)It is highest when the rock is at the lowest elevation.
B)It is highest when the rock is at the highest elevation.
C)The tension is constant as the rock moves around in a circle.

Question 42

A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite would be:

A)V
B)2V
C)V
D)V/
E)V/2

Question 43

A satellite of mass M takes time T to orbit a planet.If the satellite had twice as much mass,the time for it to orbit the planet would be:

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

Question 44

For astronauts in space,there is no atmosphere to slow their orbit.Why don't they just fly away to the moon?

Question 45

If Earth had twice as much mass as it now does but were also twice its present diameter,the acceleration due to gravity at its surface would be the same as it is now.

Question 46

Can a satellite be in an elliptical orbit under uniform circular motion?

Question 47

A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down.She whirls the rock at the minimum speed (constant in time)such that the string is always taut (no sag).If she were to use a longer string,she would have to whirl the rock at a

A)higher velocity.
B)lower velocity.
C)the same velocity.

Question 48

If you stood on a planet having a mass four times higher than Earth's mass,and a radius two times longer than Earth's radius,you would weigh

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

Question 49

If the Moon were twice the distance from Earth than it currently is,the amount of time it would take to go around Earth would be roughly (the current orbital period of the Moon is four weeks)

A)11 weeks.
B)eight weeks.
C)six weeks.
D)88 weeks.

Question 50

If an astronaut were exactly half way between Earth and the Moon,the net gravitational force exerted on the astronaut by these two objects would be

A)directed toward Earth.
B)zero.
C)directed toward the Moon.

Question 51

You need to make a sharp turn on a flat road,making a radius of curvature of 15 meters.How does the required force of static friction between your tires compare if you make the turn at 30 mph vs.60 mph?

A)The force of friction needs to be four times as large.
B)The force of friction needs to be twice as large.
C)The force of friction is the same for both speeds since the radius of curvature is the same.
D)None of the above

Question 52

A mass on a string is swung in a vertical circle at a constant speed.The string will break if the tension in the string exceeds a critical value.At what part of the circle is the string most likely to break,and why?

Question 53

Astronauts in orbit are weightless,but they are not beyond the pull of Earth's gravity.How can this be?

Question 54

Explain,from a force standpoint,why you need to reduce your normal driving speed around curves when it rains.

Question 55

If the mass of Earth and all objects on it were suddenly doubled,the acceleration due to gravity at the surface would become 4 times what it is now.

Question 56

How is it possible for someone to remain in her seat (without any straps)while upside down on a loop-the-loop roller coaster?

Question 57

In uniform circular motion we have an acceleration and the speed doesn't change.But in projectile motion the speed does change under constant acceleration.Why are they both classified as uniform acceleration phenomena?

Question 58

If I set the car cruise control at a certain speed and take a turn,the speed will remain the same.So,why am I accelerating?

Question 59

If there is no such thing as a centrifugal force,why does someone in a car making a turn feel as if he or she is being pulled toward the outside of the curve?

Question 60

A merry-go-round is spinning at a fixed rate.As a person is walking toward the edge,

A)the force of static friction must increase in order for the person not to slide off.
B)the force of static friction must decrease in order for the person not to slide off.
C)the force of static friction such that the person does not slide off remains the same.