Question 1

$$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \
\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \
\hline \text { Moon B } & 1.5 \times 10 ^ { 2 } 0 \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \
\hline
\end{array}$$ 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? (G = 6.67 × 10-11 N ∙ m2/kg2)

Accepted Answer

A) 0.10 m/s2 
B) 0.15 m/s2 
C) 0.20 m/s2 
D) 0.25 m/s2 
E) 0.30 m/s2

Question 2

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)

Accepted Answer

The answer of A very dense 1500-kg point object (A)and...

Question 3

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

Accepted Answer

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 4

Europa,a satellite of Jupiter,has an orbital diameter of 1.34 × 109 m and a period of 3.55 days.What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2)

Accepted Answer

A) 1.53 × 1027 kg 
B) 1.65 × 1027 kg 
C) 1.07 × 1027 kg 
D) 1.89 × 1027 kg 
E) 3.08 × 1027 kg

Question 5

At a given point above Earth's surface,the free-fall acceleration is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the altitude of this point above Earth's surface? (G = 6.67 × 10-11 N ∙ m2/kg2,Mearth = 5.97 × 1024 kg,Rearth = 6.38 × 106 m)

Accepted Answer

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

Question 6

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?

Accepted Answer

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

Question 7

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?

Accepted Answer

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

Question 8

What would be the gravitational force that a planet twice as massive as Earth and having twice Earth's radius exerts on a 59.1-kg astronaut?

Accepted Answer

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

Question 9

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?

Accepted Answer

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

Question 10

The average distance from Earth to the sun is defined as one astronomical unit (AU).If an asteroid orbits the sun in 1/3 of a year in a circular orbit,the asteroid's distance from the sun is closest to

Accepted Answer

A) 0.19 AU. 
B) 0.48 AU. 
C) 2.1 AU. 
D) 5.2 AU. 
E) 0.33 AU.

Question 11

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?

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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 14

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.

Accepted Answer

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 15

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)

Accepted Answer

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 16

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)

Accepted Answer

The answer of What is the magnitude of the gravitational...

Question 17

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?

Accepted Answer

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

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Exam 5: Circular Motion

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

Europa,a satellite of Jupiter,has an orbital diameter of 1.34 × 10⁹ m and a period of 3.55 days.What is the mass of Jupiter? (G = 6.67 × 10^-11 N ∙ m²/kg²)

At a given point above Earth's surface,the free-fall acceleration is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ 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)

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?

What would be the gravitational force that a planet twice as massive as Earth and having twice Earth's radius exerts on a 59.1-kg astronaut?

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?

The average distance from Earth to the sun is defined as one astronomical unit (AU) .If an asteroid orbits the sun in 1/3 of a year in a circular orbit,the asteroid's distance from the sun is closest to

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?

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?

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?

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)

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?

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?

Exam 5: Circular Motion

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

Europa,a satellite of Jupiter,has an orbital diameter of 1.34 × 109 m and a period of 3.55 days.What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2)

At a given point above Earth's surface,the free-fall acceleration is equal to 7.8 m/s27.8 \mathrm {~m} / \mathrm { s } ^ { 2 }7.8 m/s2 What is the altitude of this point above Earth's surface? (G = 6.67 × 10-11 N ∙ m2/kg2,Mearth = 5.97 × 1024 kg,Rearth = 6.38 × 106 m)

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?

What would be the gravitational force that a planet twice as massive as Earth and having twice Earth's radius exerts on a 59.1-kg astronaut?

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?

The average distance from Earth to the sun is defined as one astronomical unit (AU) .If an asteroid orbits the sun in 1/3 of a year in a circular orbit,the asteroid's distance from the sun is closest to

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?

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?

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?

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)

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?

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?

Europa,a satellite of Jupiter,has an orbital diameter of 1.34 × 10⁹ m and a period of 3.55 days.What is the mass of Jupiter? (G = 6.67 × 10^-11 N ∙ m²/kg²)

At a given point above Earth's surface,the free-fall acceleration is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ 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)

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)