Question 1

The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 10 distance units apart. If you were an astronaut between the Earth and Moon at how many distance units from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?
A) 81 units
B) 9 units
C) 19 units
D) 1 unit

Accepted Answer

The gravitational force is inversely proportional to the square of the distance from the mass causing the attraction. Let $x$ be the distance from the Earth where the gravitational forces are equal. Since the Earth is 81 times as massive as the Moon, and if we consider the total distance between the Earth and Moon to be 10 units, the forces will balance when the distance from the Earth is such that $x^2$ is to $(10-x)^2$ as 1 is to 81, because the force is proportional to the mass and inversely proportional to the square of the distance. Solving this proportion gives $x = 1$ unit from the Earth.

Question 2

The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 240,000 miles apart. If you were an astronaut between the Earth and Moon at what distance from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?
A) 216,000 mi
B) 2963 mi
C) 24,000 km
D) 24,000 miles

Accepted Answer

The gravitational force is equal when the ratio of distances from the two bodies is the square root of the ratio of their masses. Since the Earth is about 81 times as massive as the Moon, the square root of 81 is 9. This means you should be 1 part from the Moon and 9 parts from the Earth for the forces to balance. Since the total distance is 240,000 miles, dividing this by 10 (1 part + 9 parts) gives 24,000 miles from the Moon, which is the same distance from the Earth where the forces balance, making option D correct.

Question 3

Suppose you are spending your weekend on roller skates trying to get momentum from somewhere. Which of the following will give you momentum in the north direction?
A) Throwing your keys southward.
B) Throwing your keys northward.
C) Bending down and throwing your keys straight up.
D) (B) or (C).

Accepted Answer

Throwing your keys southward will give you momentum in the opposite direction, which is north, due to the conservation of momentum.

Question 4

You are substitute teaching for your spouse and are using balloons to demonstrate how rockets work. The balloons are blown up and released so that the air can leave them rapidly. Why do the balloons fly all around, even though the balloon does not have a surface to push against?

Accepted Answer

The answer of You are substitute teaching for your spouse...

Question 5

Suppose your instructor staggers into class the morning after an all-night excellence in classroom humor workshop. He proceeds to do a demonstration in class where he measures a 6.67 N gravitational force of repulsion between two particles each having a mass of 1 kg and separated by 1m. Moreover he cuts the distance to 0.1 of what it originally was and then claims the force changes to a new value of 0.667 N. Specific to the scientific content of his demonstration please briefly describe three important concepts he incorrectly illustrated (there's more than three, trust me). One of your three points must be quantitative - involving a force calculation of some sort.

Accepted Answer

The answer of Suppose your instructor staggers into class the...

Question 6

Suppose you have two identical particles that attract each other with a certain gravitational force. Now you move them so they are three times as far apart as they were originally, but the force between them stays the same. What is one way in which the masses might change so the force could remain constant?

Accepted Answer

The answer of Suppose you have two identical particles that...

Question 7

Consider astronauts orbiting the earth in the space shuttle.
-The acceleration of gravity in the orbiting space shuttle is over 90% that on the surface of the earth but the astronauts still feel weightless (no apparent weight) please explain. You may assume the orbit is perfectly circular.

Accepted Answer

The answer of Consider astronauts orbiting the earth in the...

Question 8

Consider astronauts orbiting the earth in the space shuttle. -Suppose that the astronauts are traveling at a speed of 1000 m/sec. What must the radius of their circular orbit be if their acceleration is 8.5 m/sec²?

Accepted Answer

The answer of Consider astronauts orbiting the earth in the...

Question 9

You and a friend are on roller skates. You are in a room and have a basketball and are standing in between two parallel walls. By touching only the ball, describe how you would make yourselves come together.

Accepted Answer

The answer of You and a friend are on roller...

Question 10

Compared to planets close to the sun, and based upon Kepler's third law of planetary motion, the length of the year of planets farther out from the sun are
A) the same
B) less
C) larger
D) more information is necessary.

Accepted Answer

Kepler's third law of planetary motion states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This means that planets farther from the Sun have longer orbital paths and slower orbital speeds, resulting in longer years.

Question 11

Comets have very eccentric orbits around the sun. Please explain why it is that they spend so little time near the earth.

Accepted Answer

The answer of Comets have very eccentric orbits around the...

Question 12

The rest energy of a 60 kg person is A) 8.4x10¹⁸ J B) 5.4x10¹⁸ J C) 1.8x10¹⁰ J D) 9x10¹⁶ J

Accepted Answer

The answer of The rest energy of a 60 kg...

Question 13

What mass has a rest energy of 100J? A) 1.1x10^-15 kg B) 3x10^-8 kg C) 3.3x10^-7 kg D) 0.01 kg

Accepted Answer

The rest energy (E) is related to mass (m) by the equation E=mc^2, where c is the speed of light (approximately 3x10^8 m/s). To find the mass that corresponds to a rest energy of 100J, rearrange the equation to m=E/c^2. Substituting E=100J and c=3x10^8 m/s, the calculation yields a mass of approximately 1.1x10^-15 kg.

Question 14

The relativistic energy of a 1000 kg car moving at 0.95 times the speed of light is A) 1000 J B) 2.8x10¹⁷ J C) 2.9x10²⁰J D) 9.3x10¹¹ J

Accepted Answer

The relativistic energy is given by E = γmc², where γ = 1/√(1-v²/c²). For v = 0.95c, γ ≈ 3.2, so E ≈ 3.2 * 1000 kg * (3x10⁸ m/s)² ≈ 2.9x10²⁰ J.

Question 15

The relativistic momentum of a 1000 kg car moving at 0.95 times the speed of light is A) 9.13x10⁸ kg m/s B) 9.13x10¹¹ kg m/s C) 3200 kg m/s D) 2.85x10¹¹ kg m/s

Accepted Answer

The relativistic momentum is given by $p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $m$ is the rest mass, $v$ is the velocity, and $c$ is the speed of light. For a car with a mass of 1000 kg moving at 0.95c, the denominator becomes very small, significantly increasing the momentum. This results in a much larger value than the classical momentum, which matches the magnitude given in option B.

Question 16

The speed at which a car must move so that its relativistic momentum is twice its nonrelativistic momentum is
A) 0.9 times the speed of light
B) ½ the speed of light
C) ¾ times the speed of light
D) times the speed of light

Accepted Answer

The answer of The speed at which a car must...

Question 17

The speed at which a car must move so that its relativistic energy is three times its rest energy is
A) 1/9 times the sped of light
B) 1/3 times the speed of light
C)  times the speed of light
D) 8/9 times the speed of light

Accepted Answer

The answer of The speed at which a car must...

Question 18

The maximum speed a rocket can achieve is
A) the speed of light
B) the speed of sound.
C) equal to the speed of its exhaust plume.
D) less than the speed of its exhaust plume.
E) greater than the speed of its exhaust plume but less than the speed of light.

Accepted Answer

The maximum speed a rocket can achieve is indeed greater than the speed of its exhaust plume but less than the speed of light, according to the principles of rocket propulsion and the limitations imposed by relativity.

Question 19

All current rockets eject stages or booster rockets as they climb from the earth's surface up to orbit. A rocket that did not eject any stages or booster rockets while climbing from the ground to orbit would
A) experience too much drag while in orbit and would be unable to remain in orbit for more than a day or two.
B) not have anything beneath the rocket on which to push and would be unable to propel itself upward after it left the launch pad area.
C) clutter the space around the earth with orbiting debris.
D) have to have a launch weight that was about 90% rocket fuel.

Accepted Answer

The reason a rocket that did not eject any stages or booster rockets would need to have a launch weight that is about 90% rocket fuel is due to the rocket equation, which dictates that in order to achieve orbit, a significant portion of a rocket's mass must be fuel. This is necessary to overcome Earth's gravity and achieve the required velocity for orbit. Staging allows rockets to shed weight as they ascend, making it more efficient to reach orbit. A single-stage-to-orbit (SSTO) vehicle, which does not eject stages, would indeed need to carry a much larger proportion of fuel relative to its total mass.

Question 20

Astronauts in a space shuttle accelerating uniformly in a straight line far away from any planet or star would
A) feel weightless.
B) feel just like there is local gravity
C) feel like they are moving very rapidly.
D) feel nothing

Accepted Answer

When a space shuttle accelerates uniformly in a straight line, the effect on the astronauts inside would mimic the sensation of gravity. This is due to the principle of equivalence in general relativity, which states that the effects of gravity are indistinguishable from the effects of acceleration. Therefore, astronauts would feel as though there is a local gravitational force acting on them, similar to being on the surface of a planet.

Quiz 4: Mechanical Objects, Part 2

The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 10 distance units apart. If you were an astronaut between the Earth and Moon at how many distance units from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?

The Earth is about 81 times as massive as the Moon. Suppose the earth and Moon are 240,000 miles apart. If you were an astronaut between the Earth and Moon at what distance from the Earth will the gravitational attraction on you from the two bodies be equal and opposite?

Suppose you are spending your weekend on roller skates trying to get momentum from somewhere. Which of the following will give you momentum in the north direction?

You are substitute teaching for your spouse and are using balloons to demonstrate how rockets work. The balloons are blown up and released so that the air can leave them rapidly. Why do the balloons fly all around, even though the balloon does not have a surface to push against?

Consider astronauts orbiting the earth in the space shuttle. -The acceleration of gravity in the orbiting space shuttle is over 90% that on the surface of the earth but the astronauts still feel weightless (no apparent weight) please explain. You may assume the orbit is perfectly circular.

Consider astronauts orbiting the earth in the space shuttle. -Suppose that the astronauts are traveling at a speed of 1000 m/sec. What must the radius of their circular orbit be if their acceleration is 8.5 m/sec2?

You and a friend are on roller skates. You are in a room and have a basketball and are standing in between two parallel walls. By touching only the ball, describe how you would make yourselves come together.

Compared to planets close to the sun, and based upon Kepler's third law of planetary motion, the length of the year of planets farther out from the sun are

Comets have very eccentric orbits around the sun. Please explain why it is that they spend so little time near the earth.

The rest energy of a 60 kg person is

What mass has a rest energy of 100J?

The relativistic energy of a 1000 kg car moving at 0.95 times the speed of light is

The relativistic momentum of a 1000 kg car moving at 0.95 times the speed of light is

The speed at which a car must move so that its relativistic momentum is twice its nonrelativistic momentum is

The speed at which a car must move so that its relativistic energy is three times its rest energy is

The maximum speed a rocket can achieve is

All current rockets eject stages or booster rockets as they climb from the earth's surface up to orbit. A rocket that did not eject any stages or booster rockets while climbing from the ground to orbit would

Astronauts in a space shuttle accelerating uniformly in a straight line far away from any planet or star would

Consider astronauts orbiting the earth in the space shuttle. -Suppose that the astronauts are traveling at a speed of 1000 m/sec. What must the radius of their circular orbit be if their acceleration is 8.5 m/sec²?