Question 1

A 25-kg box is sliding down an ice-covered hill.When it reaches point A, the box is moving at 11 m/s.Point A is at the bottom of a circular arc that has a radius R = 7.5 m.What is the magnitude of the normal force on the box at Point A? 
A)250 N
B)280 N
C)400 N
D)650 N
E)900 N

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Question 2

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete.
-What is the radius of the curve that the plane follows in making the turn?
A)280 m
B)350 m
C)830 m
D)1100 m
E)1600 m

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Question 3

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 10³ m/s for a 0.15-m long carbon rod.What was the period of rotation of the rod? A)7.4 × 10^-⁵ s B)3.1 × 10^-⁴ s C)4.7 × 10^-⁴ s D)5.2 × 10^-³ s E)1.3 × 10^-³ s

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Question 4

A plane is traveling at 200 m/s following the arc of a vertical circle of radius R.At the top of its path, the passengers experience "weightlessness." To one significant figure, what is the value of R? 
A)200 m
B)1000 m
C)2000 m
D)4000 m
E)40 000 m

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Question 5

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Determine the magnitude of the net force that acts on the vehicle. A)390 N B)1800 N C)8.5 × 10³ N D)1.5 × 10⁴ N E)zero newtons

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Question 6

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Jupiter has a mass that is roughly 320 times that of the Earth and a radius equal to 11 times that of the Earth.What is the acceleration due to gravity on the surface of Jupiter? A)2.7 m/s² B)9.8 m/s² C)26 m/s² D)87 m/s² E)260 m/s²

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Question 7

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m.
-Which statement is true concerning this vehicle?
A)The velocity of the vehicle is changing.
B)The vehicle is characterized by constant velocity.
C)The vehicle is characterized by constant acceleration.
D)The vehicle has a velocity vector that points along the radius of the circle.
E)The vehicle has an acceleration vector that is tangent to the circle at all times.

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Question 8

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.  Note these arrows: 
-At the instant shown in the drawing, which arrow indicates the direction of the acceleration of the rocket?
A)1
B)2
C)3
D)4
E)5

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Question 9

A small car of mass M travels along a straight, horizontal track.As suggested in the figure, the track then bends into a vertical circle of radius R. -Which one of the following expressions determines the minimum speed that the car must have at the top of the track if it is to remain in contact with the track? A)v = MgR B)v = 2gR C)v² = 2gR D)v² = gR E)v = gR

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Question 10

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.  Note these arrows: 
-Suppose that the radius of the circular path is r when the speed of the rocket is v and the acceleration of the rocket has magnitude a.If the radius and speed are increased to 2r and 2v respectively, what is the magnitude of the rocket's subsequent acceleration?
A) 
B)2a
C)a
D)4a
E)8a

Accepted Answer

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Question 11

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle.The rope will break when the tension exceeds 450 N.What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?
A)24 m/s
B)12 m/s
C)32 m/s
D)16 m/s
E)38 m/s

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Question 12

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete. -What is the magnitude of the centripetal acceleration during the turn? A)zero m/s² B)6.9 m/s² C)8.1 m/s² D)9.8 m/s² E)12 m/s²

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Question 13

A spaceship is in orbit around the earth at an altitude of 12 000 miles.Which one of the following statements best explains why the astronauts experience "weightlessness?"
A)The centripetal force of the earth on the astronaut in orbit is zero newtons.
B)The pull of the earth on the spaceship is canceled by the pull of the other planets.
C)The spaceship is in free fall and its floor cannot press upwards on the astronauts.
D)The force of gravity decreases as the inverse square of the distance from the earth's center.
E)The force of the earth on the spaceship and the force of the spaceship on the earth cancel because they are equal in magnitude but opposite in direction.

Accepted Answer

"Weightlessness" is experienced by astronauts in orbit because the spaceship is in free fall around the earth. In other words, the gravitational force is still acting on the astronauts, but they are falling towards the center of the earth at the same rate as the spaceship. Therefore, the floor of the spaceship cannot push upwards on the astronauts, making them feel weightless.

Question 14

A space station is designed in the shape of a large, hollow donut that is uniformly rotating.The outer radius of the station is 350 m.With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e.an acceleration of 9.8 m/s²? A)230 s B)170 s C)110 s D)76 s E)38 s

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Question 15

A small car of mass M travels along a straight, horizontal track.As suggested in the figure, the track then bends into a vertical circle of radius R. -What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track? A)4.9 m/s², downward B)4.9 m/s², upward C)9.8 m/s², downward D)9.8 m/s², upward E)19.6 m/s², upward

Accepted Answer

For the car to remain in contact with the track, the normal force on the car must be non-zero at the top of the track. This means that the gravitational force must be balanced by a centrifugal force. At the top of the track, the car is moving in a circular path of radius R with a velocity of v=√(2gR), where g is the acceleration due to gravity. Therefore, the minimum acceleration that the car must have at the top of the track is given by a=v^2/R=2g, which is downward. So, the correct answer is C) 9.8 m/s^2, downward.

Question 16

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -What is the magnitude of the acceleration of the vehicle? A)5.7 m/s² B)0.26 m/s² C)9.8 m/s² D)1.2 m/s² E)zero m/s²

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Question 17

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m.
-What is the average velocity of the vehicle during one revolution?
A)8.0 m/s
B)12 m/s
C)26 m/s
D)44 m/s
E)zero m/s

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Question 18

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.  Note these arrows: 
-At the instant shown in the drawing, which arrow shows the direction of the reaction force exerted on the planet by the rocket?
A)1
B)2
C)3
D)4
E)5

Accepted Answer

According to Newton's third law, for every action, there is an equal and opposite reaction. As the rocket exerts a force on the planet to keep it in circular motion, the planet exerts an equal and opposite reaction force on the rocket. This reaction force is always directed towards the planet and is perpendicular to the velocity of the rocket. Arrow 2 shows the direction of this reaction force.

Question 19

The radius of the earth is 6400 km.An incoming meteorite approaches the earth along the trajectory shown.The point C in the figure is 6400 km above the earth's surface.The point A is located at the earth's center.At point C, what acceleration would the meteorite experience due to the earth's gravity? A)9.8 m/s² toward A B)2.5 m/s² toward A C)2.5 m/s²toward B D)5.0 m/s² toward B E)5.0 m/s²toward A

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Quiz 5: Dynamics of Uniform Circular Motion

A 25-kg box is sliding down an ice-covered hill.When it reaches point A, the box is moving at 11 m/s.Point A is at the bottom of a circular arc that has a radius R = 7.5 m.What is the magnitude of the normal force on the box at Point A?

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete. -What is the radius of the curve that the plane follows in making the turn?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 103 m/s for a 0.15-m long carbon rod.What was the period of rotation of the rod?

A plane is traveling at 200 m/s following the arc of a vertical circle of radius R.At the top of its path, the passengers experience "weightlessness." To one significant figure, what is the value of R?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Determine the magnitude of the net force that acts on the vehicle.

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Jupiter has a mass that is roughly 320 times that of the Earth and a radius equal to 11 times that of the Earth.What is the acceleration due to gravity on the surface of Jupiter?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Which statement is true concerning this vehicle?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow indicates the direction of the acceleration of the rocket?

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle.The rope will break when the tension exceeds 450 N.What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete. -What is the magnitude of the centripetal acceleration during the turn?

A spaceship is in orbit around the earth at an altitude of 12 000 miles.Which one of the following statements best explains why the astronauts experience "weightlessness?"

A space station is designed in the shape of a large, hollow donut that is uniformly rotating.The outer radius of the station is 350 m.With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e.an acceleration of 9.8 m/s2?

A small car of mass M travels along a straight, horizontal track.As suggested in the figure, the track then bends into a vertical circle of radius R. -What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -What is the magnitude of the acceleration of the vehicle?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -What is the average velocity of the vehicle during one revolution?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow shows the direction of the reaction force exerted on the planet by the rocket?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 10³ m/s for a 0.15-m long carbon rod.What was the period of rotation of the rod?

A space station is designed in the shape of a large, hollow donut that is uniformly rotating.The outer radius of the station is 350 m.With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e.an acceleration of 9.8 m/s²?